Groceries: Depends where you are staying! There is an Acme near both bridges, both of which are good, and there is a Shop Rite in Marmora if you're coming in over the 34th Street Bridge. There are also some little markets, Blitz's, that might be nearby if you find you need something quick.
Restaurants: We tend to eat in (we're a big group when we go to OC!) but when we go out, it tends to be outside of OC as we like to enjoy adult beverages when we go out.

There are some great spots in Avalon (we like Diving Horse) and Steve & Cookies in Margate. These probably aren't the most family-friendly, though. The Anchorage Tavern right over the bridge in Somer's Point would probably work for a family, though -- their food is good! Same for Doc's Place.
For tweens, the waterparks in Wildwood might be fun. OC also has kayak and standup paddle board rentals that might be good for the bay.
Enjoy!!