Billy Goat Hill would be a definite five stars in most other US cities, but I can't go passing out…read morefive-star San Francisco-park reviews like candy, and the swing no longer exists and/or works, and the swing was/would be what got this review to five stars.
But Billy Goat Hill, man. It's difficult to overestimate just how surprising it is as a San Francisco park. It's not overbuilt, overthought, or annoying. Do you know how much of San Francisco is all three of those things? And especially some of its parks?
No, the hill is just that: a hillside that was spared from construction, probably because of the complicated nest of streets and elevations at its lower, northern end.
The best way to appreciate it is to come in the afternoon. If you really want to unspoil the surprise, drive east on Addison Street past Walter Haas Park. Turn right on Everson Street and then left on Beacon Street. Right after the houses end on the north side of Beacon Street, park your car. The view of downtown is amazing. Give yourself a little bit of time up on the street before you go down the path and stairs.
After that initial stunning view, the rest of the park can feel anticlimactic. It's not really maintained as a green-grass park; it's just a more-or-less feral hillside with some iconic trees, some rocky ground, and wooden box steps and handrails that have seen better days. The path goes down the hill to Laidley Street. It's fairly steep, so if you're bringing someone with mobility issues, they should either not go all the way down, or you should drive and pick them up--which is its own issue because although it's only down the hill, it is impossible to drive to the bottom of the park without going three or four times the distance.
From where you parked on Beacon Street, continue west and turn right at Diamond Street. Then turn right again onto 29th Street. Turn right on Castro Street, and when it dead-ends at the park, turn left onto 30th Street. The path at the bottom of the park ends near the weird intersection of 30th & Laidley Streets. Oh, and that "dead end" of Castro Street isn't really where it ends--after a long gap, it reappears in Glen Park for a little more than a block between Bemis and Chenery Streets, where it ends for good.
It gets really windy up here, and there are no real places to sit, so it's more of a short-hike park than a hanging-out park. Still, it can be serene to just sit in your car and take in the view, which never gets old. Another fun part is looking almost due east from the promontory and seeing Bernal Hill also standing out beautifully and boldly in the city. I'm sure you can see Billy Goat Hill from Bernal Hill as well.
I've been many times on beautiful, fog-free days, and I've never had trouble finding street parking right on Beacon Street. There's regular street sweeping, of course, but I'm really surprised it's not more crowded with cars.