When I lived in San Francisco, I often found myself with a hankering to get a bit of upper-body exercise on weekends by doing pull-ups. I didn't live particularly close to the gym where I had a membership, though, and I felt dumb paying five bucks to stop in at the Buchanan YMCA. (The Koret Center at USF is a decent option if you live near the area, although their prices seem to be going up.) As such, I kept an eye out for horizontal bars in the seven-to-nine-feet-off-the-ground range that looked like they could support my weight. If you live in San Francisco and have a similar mindset (and even if you're a bicep-obsessed chin-up enthusiast or a kipping-crazed Crossfitter), I hope that you find this list helpful.
The Castro, the Mission, and SoMa seem to be surprisingly underserved in the pull-up bar department, but there are plenty of options if you're in the Western Addition, the Richmond, or especially the Marina. And if you've found any other good spots that are open to the public, let me know!
Near the entrance to the de Young Museum in Golden Gate Park, there's a collection of bronze sculptures by Arthur Putnam. Think somewhat-blobby-looking animals attacking other animals, a boy wrestling a hare, etc. Each sculpture is housed in a small cage, but those cages are themselves located in two larger cage-like structures.
The bars along the tops of the structures are at just the right height for a tall person or a good jumper to spring up and grab them, and they're spaced such that it can be fun to swing between them monkey-bars-style. Benches line the structures, likely making it possible for shorter folks to also get up to the bars. I'd estimate the wider bars to be around three inches in diameter.
Families occasionally stroll by to look at the sculptures, but in general, the area is mostly deserted on weekends. The eastern half of Golden Gate Park is closed to vehicular traffic on Sundays; if you're coming from somewhere to the east, you can bike, jog, or walk through the Panhandle and then have John F Kennedy Drive all to yourself after you cross Stanyan.
The Perrier Parcourse surrounds the Golden Gate Park Polo Fields. I vaguely remember visiting a similar parcourse in my small hometown when I was a child; the general idea is a golf-course-style circuit of workout stations. Each station is constructed from unadorned logs and steel bars and has a placard describing an exercise that can be performed at one of three different difficulty levels.
Given the courses' provenance in the early 1970s, it's unsurprising that many of the stations instruct participants to perform calisthenics. Near the end of the Perrier Parcourse, there are several stations where pull-ups and related upper-body exercises can be performed, though. Following a trail into the wooded area to the east of the track, one arrives at a station consisting of a triangular arrangement of vertical posts with three steel bars joining them at different heights. Each bar has a pair of rings hanging from it, but it's also possible to do pull-ups on the lowest bar. If you're feeling adventurous, you can try to start from a dead hang facing outwards at the left edge of the lowest bar, launch yourself up and grab the medium-height bar with your left hand, work your way hand-over-hand to the left edge of the medium bar, and then launch yourself up to the highest bar. My success with this maneuver is hit-and-miss.
Following the same trail to the east, the next station is actually intended for pull-ups. There's the same arrangement of three posts with bars between them, but the bars here are narrower and closer to the ground. Around the north and west sides of the track, there are stations where one can do push-ups, sit-ups, and dips.
I usually don't see many people at the parcourse on weekend mornings.
I still can't figure out what the National Fitness Campaign is, but they have a quite good fitness court in Marina Green Triangle. At the spot where Webster Street meets Marina Boulevard, just east of Marina Green proper, you'll find a modern-looking, blue-and-gray structure with various fitness stations. Along with a large assortment of bars and rings, there are a few boxes that one can use to work on jumps.
Unlike the previous recommendations, this fitness court has had a decent number of people using it whenever I've visited it. There are enough stations that finding one to do pull-ups at has never been a problem, but if you shy away from exhibitionism, you might want to stay clear (the court is just a block away from the Dateway, after all). There are also occasionally trainers/clients and boot camps here.
Just north of the fitness court in Marina Green Triangle, there's another parcourse station. It looks like it has bars for doing both pull-ups and dips, but to be honest, with the fitness court so close to it, I've never tried using this one.
If you head north on the path that starts at the point where Baker Street meets Marina Boulevard, you'll quickly come across another triangular parcourse station with two sets of rings and a swinging bar at various heights. I think that this is part of the same parcourse as the bars in Marina Green, but it's hard to be sure since the various stations are all spread apart. Thanks to Pamela Carrara for pointing these out!
How many pull-up bars can a single neighborhood need? In the case of the latissimi-dorsi-obsessed Marina District, the answer is, "a lot". Just southeast of Marina Green Triangle, between Fort Mason's Great Meadow and the Octavia-Bay three-way intersection, there are three pull-up bars of varying heights. Rather than using the standard triangular setup seen elsewhere in San Francisco, the bars are arranged in a "C" configuration using four posts. They're plenty sturdy. No gripes here, although I wish that some of the fitness-equipment love would be shared with the rest of the city.
Mountain Lake Park lies between the Richmond and the Presidio, just east of Park Presidio Boulevard. It was under construction when I visited it and is fairly noisy due to the boulevard, which runs just to the west of the lake.
A parcourse runs in a loop south of the lake, starting near the park's entrance at Lake Street and 9th Avenue. The stations are similar to the ones in the Golden Gate Park parcourse, although the construction quality at Mountain Lake Park seems lower. At the pull-up station, located just to the west of the shelter that can be seen to the north of the entrance, all three bars were visibly sagging. I'm a skinny guy, but the tall bar still bounced and creaked under my weight. If I weighed more than 200 pounds, I'd be concerned about the bolts giving way. Someone had put tape on the highest bar, which was a nice touch.
Following the trail east from the pull-up station, there's a triangular arrangement of rings similar to the one in Golden Gate Park. The bars here seem sturdier than the bars at the pull-up station, and they're also narrower than the ones at Golden Gate Park.
Sunset Circle is a parking lot to the north of Lake Merced, just south of the point where Sunset Boulevard meets Lake Merced Boulevard. It can make for a nice bike ride, although the weather is unpredictable (okay, that's a lie; you can usually count on it being foggy) and the western half of the city is awfully car-oriented.
To get there from the east side of the city:
Along with a statue of Juan Bautista de Anza on a horse, Sunset Circle has a set of three sturdy pull-up bars at varying heights. I suspect that it may be part of a larger parcourse (although I didn't see any signs) — a bit to the west, there's a body curl station.
Around this diminutive park's perimeter runs a miniature parcourse where multiple exercises are crammed into each station. At the southwest corner, there are pull-up bars. To the northeast, there are rings. The northwest corner has parallel bars for doing dips. All of the equipment seems decent enough. You'll need to put up with the constant roar of traffic on nearby I-280, but I think that this park may be your only nearby option if you live in the Dogpatch or the Mission.
The Candlestick Point State Recreation Area is located to the east of where Candlestick Park1 (or Monster Park2 or 3Com Park, depending on which way the wind is blowing) used to be. While it's far from the nicest bike ride that I've taken in the Bay Area, the recreation area is relatively easy to get to from downtown: head east on Cesar Chavez across 101, turn right onto Evans Ave heading southeast, take another right onto 3rd St heading south, and then turn left onto Gilman Ave at the Paul Ave / Gilman Ave intersection. Gilman wraps around the east side of the former park area and you'll see several entrances to the recreation area to your left.
Rather than being an official Parcourse, the Candlestick fitness trail is a "For Seniors" Wells Fargo Gamefield Walking Course. Many of the stations are low-effort (e.g. standing push-ups), but there's an unexpected, unlabeled set of pull-up bars several stations in. There are thin-but-sturdy bars at three different heights arranged in a row.
Hayes Valley Playground is located on the south side of Hayes Street between Buchanan and Laguna. Along with the titular playground, it includes basketball and tennis courts and a whole bunch of Parcourse-style fitness stations for adults. I haven't paid it enough of a visit yet to scope out all of the equipment, but the pullup/dip station seems well-constructed.
Franklin Square's playground is located at the northeast corner of Bryant and 17th St. Per Stefan Roesch, who spotted it, "it does say you have to be 'accompanied with a child' but normally this playground is empty in the evenings so..."
Trouble Coffee's Yosemite Ave location hosts a parklet with bars of a convenient height. Again per Stefan Roesch, "these are perfect for pull-ups and you often see people monkeying around on them".
Jacopo Bergese mentioned that Mission Playground, located in the block between 19th and 20th Streets and Guerrero and Valencia, has several bars that can be used for doing pull-ups. I don't think that adults are allowed in the playground without children, but if you have a kid with you (or are there in the morning or evening, when Jacopo suggests it's often empty), this may be an option for you.
Shelley Wu pointed out that Father Alfred E. Boeddeker Park, at the corner of Jones and Eddy Street in the Tenderloin, has outdoor fitness equipment including a station for doing pull-ups and dips. The Trust for Public Land has a page with a video with more information about the creation of the park.
Many traffic lights in San Francisco have pedestrian walk/don't-walk signals situated on sturdy crossbars that are at a good height for doing pull-ups. You're likely to get some stares or comments, but if you don't have any other options near you...
Much of the scaffolding that's erected on the sidewalk while construction work or painting is being done has bars that are around the right height for doing pull-ups. Keep your eyes peeled; you may be lucky enough to have some near you.
I feel a bit self-conscious when using scaffolding doing pull-ups, though, along with fearing that passersby will suspect that I'm trying to climb up to break into the building that's being worked on. If that doesn't bother you, though, go for it.