Planning a day trip to York with kids

[ILikePaperHats]

Hi I'm planning a day trip on train from Sheffield to York with my two DSs aged 6 and 12 on Sunday. We have been to the Castle museum and the Railway museum before. Do you think York Minster is a good idea or would they just be bored? Are there any other things we could do that won't cost too much? I think York Dungeons might be too scary for them but not sure. I did think taking them to Betty's tea rooms might be a nice treat but they will probably just scoff the cakes and not eat the savoury stuff as they're not keen on sandwiches! Any other ideas of where to take them for lunch? Any tips appreciated thanks

My niece at about 7 adored the Jorvik centre and Clifford’s Tower.

Thanks everyone. Some good suggestions there but will probs be too cold for boat trip/walking the walls. And I can see my 12 yr old being bored by the latter. Shame the Minster is so expensive.
What's the ice trail all about?

It was on at the weekend. There were loads of ice sculptures dotted around York and a live carving demo. I think they do it every year.

I've cropped dh and dc out of this but it's one of the sculptures from the trail this weekend.