If you can tear the kids away from the beach and pool in time, many places have early dining specials that can be a good value. A couple that come to mind are Lobster Shanty and Mr. Manatee's which are both located in Royal Palm Point in Vero. Both are also on the water so you might see manatees or dolphins if you have a table by the window.
Johnny D's Bistro has some good deals, especially their Prix Fixe menu. They're a bit further south on A1A.
For pizza/subs/pasta Vittorio's at US1 and Barber Rd. in Sebastian is yummy and definitely family friendly. They're closed Sunday but tend to have good specials Monday and Tuesday. Even when they don't have specials, they're a good value.