If you are there over the holidays, lots of places have kids eat free with an adult main, including Tomahawk Steak House, Impossible Bar and Bills.
We enjoy the very bold squirrels and a walk in the museum gardens then getting an ice cream from the boat on the river next to the gardens.
There are private hire boats on the river, we plan to do them in a week or two (we are a short train journey away so go most school holidays).
not sure if anybody has mentioned Wonderlab at the train museum but both mine enjoyed that (boys aged 9 and 11). I would aim to get there early for that one as we went when it was crowded, still good but would be better when quiet.
There is also a supposedly haunted pub, I think it is the Golden Fleece, which is great, the rooms are all wonky and there are little spooky touches.
The castle museum and the chocolate story have both been a hit with mine, you get lots of samples as you do the chocolate story.
if you have a car, you could also do Castle Howard, Fountains Abbey, LightwaterValley, Flamingo Land (look for vouchers on line for that one).