Thanks for the info people, sounds like a great place to chill out and go exploring.
I'm in two minds (ok more like 99.9% sure - just needing to secure the ring) to propose as well, any magical places you could think of in York, what would be the perfect spot?
If you're going to propose in York, do it near the Minster at night. It is absolutely beautiful when it is all lit up.
Places to go are so many to list. For food, Oscars used to be good but isn't quite as good as it used to be. El Gaucho as has already been mentioned has fantastic food (steaks mainly, and not to be confused with the London chain as they aren't the same). Also there are a lot of good Indian restaurants like The Viceroy (on Monkgate), and a lot of nice little Italian restaurants along the way too. Don't go to Jumbo's for chinese though. It is rather rank. You can literally walk into town near the Minster and pass so many nice places for food and drink.
The weather has been fantastic over the past few days, although it is raining here at the moment but I believe that it will stop for the weekend. Having drinks down near the Ouse (Kings Arms pub, which floods every year, is a very famous York pub) is nice and it is right on the river's edge. You can then have a nice stroll all the way down the river toward Fulford, one of the outer-lying villages that is attached to York now.
As for things to do, I highly recommend the Dungeons, as well as the Castle Museum if you're interested in a bit of history.
For a night out, you can't go far wrong with a bar run down Micklegate and into town. It is pretty much bustling with everyone in York as it is a well-known crawl.
Finally, as has been said, go for a walk around the city walls. They're still in great condition and make for an interesting time as they weave all the way in and out of a lot of the main parts in the centre of York.
Your hotel is practically in the centre of York. If you're arriving by train it is about 10 seconds away from platform one (I think it is)