The resort offers all kinds of activities, in addition to its swimming pool, miniature golf course, and tennis courts. Make sure you look at the activity sheet when you check in because some require that you sign up in advance.
Also near the front desk is a table with books containing some menus and directions to area restaurants, with copies of the directions to take with you. The resort itself has a couple of restaurants -- Shutters and Sonyas. You also can get sandwich and snack food at the pool and in the Green Cabin Room, which is a lounge in the Inn with a nice view of the ocean.
Other potential things to do/places to see are:
McLarty Museum depicting history of the Spanish fleet that sunk off the Vero-area coast; Mel Fisher's Treasure Museum showing stuff recovered from the 1715 ship, the Atocha; shopping in boutiques and an outlet mall; golf at area golf courses; exhibits and boat tours at the Harbor Branch Oceanographic Institution; tour of airplane production at Piper Aircraft; nature tours and canoeing on the Indian River Lagoon at the Environmental Learning Center; tour the McKee Botanial Garden; see an LA Dodger spring training game at Dodgertown's Holman Stadium (assuming you visit in the spring). There's also an AMC movie theater nearby, a professional theatre and an arts center. The Guest Services at the resort can help you with more information on these things, and has a map on how to find them.