Your budget is good for a new, good quality commuter BUT if the university is a high bike-theft zone that's quite a lot. In high crime areas I would prefer to ride a decent older bike bought used. Include rack, fenders and light, bags and lock in your budget.

You need to know your distance, terrain and load before chosing a bike. SF has some steep hills so you may need a triple chainring.

Any std, non-suspension hybrid will do the job as will touring and road-sport bikes. Road race bikes are probably too highly geared and lack rack/fender eyelets.

Decide what you want to do with the bike when your not commuting: riding local roads or trails. If trail riding is your thing, an MTB will do dual duty.