There isn’t actually a whole lot right around the Bay Area. One of my favorite mountains is Mt. Shasta, which is a shot up highway 5 north and is an excellent and cheap place to learn how to ski. The drive up 5 isn’t that bad either. If you don’t mind paying a bit more, though, check out the Tahoe area. A comparable drive to Shasta, but definitely nicer mountains. It is quite a bit pricier, though.