We were at Vero in July, and pretty much stayed on the property for the week. However, we did venture out one night to Captain Hiriam's and thought it was a good meal and fun atmosphere. We also ate at all of the choices at the resort - Bleachers has pizza you can take back to your room or eat by the pool, as well as good quick sandwiches (I liked the chicken salad platter for lunch!), Shutters has a small menu, but it was good, the Green Cabin Room has a great view if you sit on the porch, and I would highly recommend Sonya's Seafood Buffet if you like seafood!
As for things to do, your younger child, at least, should find the teen activities to be a fun way to spend the evening - they do campfires for the teens, as well as other things.
We also rented waverunners and had a blast! They also rent sailboats. Either rent or take boogie boards with you too (we bought some at
WalMart for about $15). I'd suggest taking a frisbee or football if your kids like that. We took our boys (and gathered others) to play an impromptu football game on the bocce lawn. The boardwalk area is a place to go at night to use the night vision goggles if you are interested in the turtles.
There is a mall with movie theatre nearby, we met some people who went, but we never made it ourselves. They also went to an outlet mall that was near.