Yer daft bugger - we're all going to Northallerton for the day!
National Railway Museum is brilliant, and free. York Castle Museum also brilliant but pricey unless you happen to be a resident with a York library card. Jorvik is, IMO, highly over-rated, and I've never bothered with the dungeons. The open-top bus is surprisingly entertaining, especially if you get a live guide instead of the crappy taped one. Minster is well worth a visit, although I believe they now charge an arm and a leg unless you're resident, and I highly recommend lying on the floor there to fully appreciate the view - of course, I can get away with these things because I usually have a small child in tow and you're allowed to do stuff like that without getting treated like the loony on the bus when you're engaging in childcare. Museum Gardens (couple of minutes from the station) is a fab place for a picnic if the weather is nice - the Yorkshire Museum (again free to residents but charge for visitors) has just been redone and I'm told it's very very nice. A cup of tea in Betty's only costs 30p more than one in BHS, and has to be done at least once IMO - their food is great if you're feeling indulgent. Lots and lots of great cafe's/bars/restaurants etc to cater for most tastes - I'm sure plenty of the Yorkies will have recommendations if you want summat in particular! A walk round the walls is well worth doing, if it isn't peeing it down (the walkways get slippy if it's raining which makes it less entertaining). I like the model railway - tiny wee thing, clearly run by obsessive geeks, pretty much in the station. We have a 'priviledge card' for that one, if it hasn't expired, that gets half price entry and a discount on everything in the shop! How long are you planning to stay for?