St. Augustine is my absolute favorite city in Florida. I second the recommendation of B&B's as opposed to hotels. Most are off of George Street, which is the main street of the historic district. I highly recommend The Agust Inn, whose owner is just a very nice and helpful person.

The one fault of St. Augustine is that St. Augustine Beach, itself, isn't very attractive. The sand is hard and the beach is bare. Drive a few miles south to Crescent Beach if you want some softer sand and prettier scenery.

I personally don't think it's a tourist trap, at least not on par with Miami or Orlando, but of course things like Ripley's Believe It Or Not, The Fountain of Youth and Alligator World do cater to the tourism market. Doesn't mean they're not worth visiting, though.