The major airports are located in Jacksonville (which is about an hour drive to the airport) and Daytona Beach (which is an hour from the south). We are about an hour away from either major airport. There are convenient shuttle services from both airports and of course rental cars are widely available. One should get to St. Augustine if you are interested in the historical side, because in the downtown historic district you don't really need a car once you get there. It's very compact; there's a number of great hotels right downtown and there are both a sightseeing trolley and a sightseeing train. For a small fee, you can buy a ticket that's good for a three day stay. You can ride continuously through the historic area getting on and off at any location that you want. So it's not one of these place where you feel like you are going to have to get the car and drive, because it's all very compact.
