Can I make a recommendation for The Acer Hotel - lovely little B&B, and maybe it'll work on you as it did for us....as the day after we stayed there we went to Whitby and I proposed!
Anyway, I'm sure if your guy is a North East bloke he'll be very familiar with York and have a few places he'd like to show you but the place is just crammed with things to see. Just a walk around the city walls, or on the riverside, the museums, the Minister etc.
Don't forget to sample a York Brewery pub either!
p.s. enjoyed reading some of your posts, how you got together and waiting for meet-ups.....took me back to this time 2 years ago when I was a few weeks from my first visit to see my, now, wife.