You'll really need to prioritise if you are only spending an afternoon in York. The Minster if you do one of their tours is an hour, Betty's is a bit of a long wait if you're going there for tea (it's in all the traveller's guides), plus there's the Shambles, the Jorvick, the dungeon, the market, Fairfax house, Museum gardens, Merchant Adventurers Hall, the Roman Baths and a ton of other places. I'd check out some of the websites about York and really think about what you want to see in that afternoon that way you won't miss something you really want to see or whatever.
I love Ripon with Fountain's Abbey. It's fab. There is also Castle Howard, where I'll be tomorrow. It's the set for Brideshead Revisited. It's quite lovely. If you are near Leeds there is also Harewood House or Temple Newsam, also two lovely big houses.
A bit farther north there is Hadrians Wall, which is fun to walk along.
I hope that helps.
And I hope you have a fun time up here. Whitby is gorgeous!