Depending on how close you live to campus and the downtown area, I think you could get away with walking and using the bus to get around. However, I would highly recommend you learn to ride a bike. If you're nervous about biking on the road, there are workshops and courses you can take through the university or town that will teach you the rules of the road and how to bike safely next to vehicles.
It's hard to say if you'll be bored by the small town experience. The university has a diverse student population and lots of multicultural clubs and events. Davis is very close to Sacramento and about a 1.5 hr drive from San Francisco, so there's lots of places to go on the weekend if you want to get out of town. Personally, I think Davis has tons to offer in terms of sports, bars, restaurants, local hiking, etc. Think positively and keep an open mind.