In addition to the onsite suggestions you've already received, we love Earl of Sandwich at DTD for very casual, inexpensive meals.
Offsite, we use two main venues -- Crossroads, just down the road from SSR (lots of choices) and Celebration.
In Celebration, our two favorites are Columbia and Kilwin's. We also enjoy walking around Celebration after dinner.
Columbia is a famous Spanish restaurant from the historic Ybor City area of Tampa. Everything on the menu is very good. Their legendary 1905 Salad (mixed at your table) is a must with every meal. Great food, great service, moderate prices.
Kilwins is a chocolatier/ice cream place. Both the chocolates and the ice cream are to die for. We usually bring home a bunch of Toasted Coconut ice cream.
We've been to the Old Town Tavern several times without really being impressed much. We'll skip it next trip.
For fine steaks, Charley's (several locations) is better than anything onsite. Less crowded, better steaks, better service, and although pricey, less expensive than the premier onsite places.