You can’t really go wrong with a decent place to drink – the whole town centre is one massive pub crawl now. Just wander around and dip into anywhere you like the look of.
Open top bus tour gets to see most of the sights easily, wander around the Minster, Railway Museum is brilliant (but I’m a bit of a train geek), plane museum out at Elvington is ok if the weather is decent, walk around the Bar Walls, walk along the river to Rowntree Park, wander around the Knavesmire… loads and loads of stuff to do and see within the inner ring road – just wander around.