Dd and I go to visit relatives every winter in St Augustine, and have a blast. This year we went to Ripley's (should be called Rip-off's, but it was all she wanted to do!) The trolley tours are very cool, there's a Gatorland, The Castillo, and as a pp mentioned, St George St. We haven't been yet, but there's also the Fountain of Youth..my rels say it's also a rip-off, but might be fun in a cheesy way. We haven't been to the lighthouse yet, but it's on our list for next year.
If you have the time/inclination, the Jacksonville Zoo is one of the top rated in the country, a lot of different types of animals, not just the usual. We went this year and enjoyed it immensely. You may want to take a picnic with you, the food isn't great, and is overpriced. If you enjoy shopping, the outlet malls are good, there's also a small flea market about ten minutes away in Elkton, which we always enjoy.
Food-wise, if you like seafood (particularly shrimp) O'Steen's is a must-do. It's a tiny, family-owned restaurant, and the fried shrimp are to DIE for! Soo good! Try to hit during off-peak hours..I promise you won't regret it- it's the place all the locals go. Hope this helps and you have a great trip
Almost forgot..O'Steen's does NOT take credit cards..cash only..but the prices are pretty reasonable..thinking 7-30 for an adult meal, depending on what you order and the quantity..six shrimp are plenty for me, but I know that can vary person to person.