GrahamG said:
Evil Eye Lounge for cocktails
Nice one, but how old is kovu?
Hmm, what sort of thing do you like? Yes, there's loads of history, but actually the city centre is pretty compact, so you can pack a lot of 'gawping at old buildings' in a short space of time. Also, are you on a budget?
So...if you like historical stuff. The Minster - costs to get in and costs more to go up the tower, but the views are good at the top. Otherwise, just wander round the outside and marvel at the fact that they had to build it with no modern power tools or whatnot. Cliffords Tower - also a charge to get in, but also good views, and the site of York's very own Jewish massacre, so a bit thought provoking. If you can spare an hour or so and don't mind a bit of a walk (and a fair few up and down steps bits) a walk of the walls gives you a good tour of the city, again, with good views. There is also the Castle Museum - York through the ages, the Yorkshire Museum (geology and natural history and archaeology) or Jorvik (viking time travel touristy gimmic) and the Dungeon (no historical value whatsoever, but a giggle). All these cost to go in. The National Railway Museum, on the other hand, is free, and even if trains aren't your thing, it's worth a wander in to see the social side of things, and the royal trains (peer in at Queen Victoria's toilet!). Plus you can see Mallard, the fastest British steam loco ever, and in the workshop, the shell of the Flying Scotman, which has bankrupted more owners than the credit crunch and is in bits AGAIN....
For more recreation: I can't remember how old you are, so I hesitate to recommend too many pubs - anyway, my taste in pubs is probably a little middle aged for you. The Shambles is a picture postcard old street (but with modern shops), and Stonegate is also a touristy sshopping street (and the Evil Eye is down there). Plenty of tea and coffee places all over the place. Coney Street has all the usual high street shops.
I'm bound to think of more, so I'll pop back when I do....