Orlando sits in the middle of Florida, which makes it a decent base for day trips. The Kennedy Space Center on the Atlantic coast is about an hour's drive east. St. Augustine, the oldest continuously inhabited European settlement in the United States, is just over two hours north — a walkable old quarter, a Spanish fort, and a long beach. Cocoa Beach and the surf breaks near Cape Canaveral are closer, 45 minutes to an hour away.
Tampa and its zoo and aquarium are a 90-minute drive west; from there it's a short hop to the Gulf-coast beaches around Clearwater. For something wilder, Blue Spring State Park 40 minutes north is one of the best spots in the state to see wintering manatees.