Within the city of Davis, bicycles are more than enough. However, if you have kids or plan to travel across the country a lot, than you might consider buying a car. The cars here are well maintained and even 10 years old car can sometimes look almost new. Cars can be bought from privet owners that advertise their used cars on craigslist, but a much simpler (and a bit more expensive) option would be to buy it from a car dealer. All you have to do is go to one of the local car dealerships, find a nice car, bargain for a good price, pay and go home with the car. The dealer will take car of all the DMV's bureaucracy.
A list of Davis car dealerships can be found on DavisWiki
Another one that is not of the DavisWiki's list: Sac River Auto