If you're staying in the states, the expanded area around Phoenix is hard to beat for weather in January and February (they don't call it the "Valley of the Sun" for nothing, after all). Cost of living is pretty low (unless you're intent on being in certain parts of the Valley) and there are plenty of good cars that haven't seen salty roads or acid rain. Older ones you're going to have to replace all the rubber and it will probably have some interior/upholstery issues, but that dry air really keeps up the chassis.

Side benefits: It's really easy to find good Mexican food. (Many other kinds, too.) Gas prices are often some of the cheapest in the nation. There are plenty of other things to see and do if you get bored wrenching on the car and you probably don't have to go far to see/do them. If you like light hiking, Piestewa Peak and Camelback Mountain are great, with excellent views of the valley. You can hit either one in the morning and be back home and showered well before lunch, good way to work the kinks out after laying under the car to change suspension parts.