We are blessed out here in Berkeley. First there is a small not really that good bouldering place called Indian Rock. It's a weird kind of metamorphic rock of some sort but has a bunch of standard routes 20 or so feet up and many much lower, some very difficult. There is a giant boulder on top of two out crops that forms a pit below. You can also practice aid off the big one on top. It's about 30+ feet. I learned the basics of prussiking, rappelling, and some rope work. That was back in the 1970s, early on weekend mornings. There is a difficult traverse across the bottom edge going from the right then up. But there is a also a trick traverse, which has an easy but scary approach route from the left. Back then, the pit got crowded after late morning. But with the development of gyms, the place was pretty much abandoned.
Then there is a related smaller group at Mortar Rock and two other places. The routes up the street at Mortar are much more difficult. These were some of the original Yosemite climber practice areas for those (Steve Roper, et al) from Berkeley and environs.
Also UCB does have good buildings to climb some of which you can rope up. But the cops come and chase you off. There is a particular style of the granite facade that has square cut edges between blocks about one and half to two inches deep that you can use. In the old back exit to the library is a wall with this facade, right next to smooth stone facade that forms a layback and hand jam. I only got up about fifteen feet which is intuitatively as far as I am going without a rope. The landing is stone, but you can land on your feet. It hurts but doesn't break anything unless you land wrong. The problem is a kind of fine dust on the stone that is a real hazard.
Another problem with climbing in Berkeley is there are some scary-good climbers around ...
CG