The Jorvik centre is a bit... popularist is perhaps the word. I like to learn a bit and I don't think you do, since they revamped it. It all hinges on the hilarity of the 'smellivision' aspect, I think... We have a 'Dungeon' too - pretty much the same as the London one I think.
Two boys? National Railway Museum!
http://www.nrm.org.uk/
Free entry, all the trains you could shake a stick at. And it's not just locos, (although there are plenty of those), there's a section on Royal Trains with examples from Victoria onwards (where else would you get to see a queen's toilet?), and there are various carriages and stuff, in two main halls. Then there's a section where they have loads of stuff they don't have room to display properly, a treasure trove of odds and ends with railway connections, all packed on shelves. And you can walk along a gantry above the workshop, and see whatever they are working on at the moment. There's a model section too.
If nothing else, it's an opportunity to be right up close to some huge locos and really appreciate their scale.
Otherwise:
The Castle museum is sort of the story of York through the ages - there's a recreated Victorian street for example. The Yorkshire Museum is the geology/archeaology/natural history type museum. Cliffords Tower is a miniature castle on a mound, good for views from the top of the walls. And the city walls themselves are worth a walk round - a couple of miles in all, but if you want to do a single section, do the bit from Monkbar to Bootham Bar, for great Minster views. The Minster of course - there an additional charge for the Tower (a very long spiral staircase up, you can see my flat from the top, so do wave in a North Easterly direction in case I'm in), or the crypt, which houses various precious metal treasures, and the enormous concrete underpinnings for the tower, just try not to think about all the weight over your head...
Even just walking between destinations can be fun, if you divert down the odd snickleway to see where it leads you - snickleways are the odd little passages that join up bigger streets, and have names like Mad Alice Court, and Lady Peckitts passageway. On the subject of streets, for the proper medieval look, do walk down the Shambles, where the houses almost meet overhead, and if you boys are the short who like a bit of gore, tell them about when it was a street of butchers' shops and all the offcuts and blood were just chucked out into the gutters....
If you have an evening free, you might want to do one of the ghost tours - I think a lot of them are suitable for children, you could enquire at the tourist office.
I'm sure there's plenty to keep you going - I could spend the best part of a day in the NRM myself, but if you find yourselves train-fatigued, the fact that it's free means you feel you have to see everything in one hit...
