Norfolk, Va

Ok!
The Naval Base tour itself is a 45 min bus ride around the base.
You can see the ships at dock from a distance but you don't actually get anywhere near them.
Nauticus & the Battleship Wisconsin is a museum that's off base in downtown Norfolk and you get to walk all over the ship.
And finally, there's a 2 hr cruise (departs from near Nauticus) that gives a harbor tour and is a better way to view the ships at dock at the base than the bus tour on the base and it's very comfortable.
The kids might really enjoy the whole thing.
It's great seeing things with Dad that he's enthusiastic about.
And on the bus tour, you have a shot at seeing a lot of nice young men in uniform or jogging on base so there's scenery for you to take in even if you are not interested in ships yourself.
Bring binoculars.

There's also the zoo, which is a good way to spend a few hours.
The Botanical Gardens are nice, (Butterfly exhibit and children s area) but some kids do get bored with it.
These are the things to do that are grouped in Norfolk.

http://www.norfolkvisitor.com/norfolknavy/
http://www.virginiazoo.org/
http://www.norfolkbotanicalgarden.org/home

If you want to get into Virginia Beach, there is the beach itself
and the Aquarium.

http://www.virginiaaquarium.com/Pages/default.aspx

The ocean?! It's basically Virginia Beach...

If your kids aren't into the Navy stuff, you can always take them to Busch Gardens in Williamsburg. It's only about an hour away and it's lots of fun.

I was going to to say, just go to Va Beach for the day. They have a nice boardwalk. Also Williamsburg is a lot of fun. You don't have to pay anything to just go there to the little historic part and you can get lunch, walk around and see all the cute little shops. You only have to pay if you are going to colonial Williamsburg area where they have the tours and people that are dressed up. But not the rest of the town.

Your kids aren't too young for Williamsburg, but if they aren't into history, they'll probably be bored.

Norfolk has a small zoo. They do charge for tickets, but its something to do.
http://www.virginiazoo.org/

Jamestown (first colony) is nearby.
Yorktown is nearby. A friend just went last week. Said they have a little beach, you can see the ships come in. Plus its an old colony so there's a bunch of historical things to do.

VA Beach is about 30 mins past Norfolk. There are tons of things to do along the boardwalk.

Great Wolf Lodge is in Williamsburg, one exit from Busch Gardens. Its a hotel/indoor waterpark. Expensive but fun.

The kids are not too young for Williamsburg at all. We went over Memorial Day weekend and my kids were 8, 7, and 5 - they loved it! We also did Busch Gardens and Water Country USA. We go yearly.

The beach is right there. If you're military, go to DamNeck and the beach is MUCH less crowded.

Ask the people at your hotel what fun stuff there is to do. I took my kids to Raleigh in March and the girl who checked us in told us of several places to go and now my kids want to move there!!

I remember there is a boat ride accross to portsmouth that the kids enjoyed.