I like Jimmy Cantler's in Annapolis on the Severn River. Everything is put down in front of you on a picnic bench with a brown paper "tablecloth" and your kids can get as messy as they want. I would have to agree with Vespa1 and say that you should come late in the season. There's plenty of great sightseeing to do in Annapolis. Also, it's true that you will not find the crabs cheap anywhere. At Cantler's, we like to order a few different things and then maybe add a dozen or so crabs to our order.
Crabs are never really cheap. Kids usually get tired of picking them pretty quickly anyway if they're not used to it so pick a restaurant where you can have a few crabs and then something else to round out the meal.
There's lots of good suggestions on this board for seafood places in or around Baltimore and your kids would probably enjoy the Inner Harbor, which has a terrific aquarium.
There are good places to eat crabs near Easton, which has a great Historic District and excellent restaurants. You could ride the Oxford-Bellvue Ferry, the oldest privately operated ferry in the US, across the Tred Avon river, and then drive to St. Michaels. The Maritime Museum is wonderful and the Historic District there has fun shops and more good restaurants. The Crab Claw restaurant is right on the docks.
More crabs are available all the way at the end of the road at Tilghman Island, one of the last of the watermen villages. Try Chesapeake House and sit out on the dock or inside for family style fried seafood.
Annapolis has the US Naval Academy and another Historic District near the State Capital if your kids are history-ed out. It's fun to wander around the docks and you'll find plenty to see and do. Lots of restaurants. It's possible to take a cruise on a sailing vessel on the Chesapeake which your kids might enjoy. Some of the cruises include meals.
All of these places have frequent postings on this board so you can see specific recommendations.
If you're looking for a cheap and fun experience, try a place on the Eastern Shore and don't come until September. The crabs will be at their best then. Early season crabs are empty and almost certainly not from Maryland and definately not worth the money. Most people in Maryland have not caught on to this fact. Late season crabs are the best of the year.