Oh, this could be a long list! For restaurants, the Bengal Brasserie on Goodramgate is consistently the best Indian. It's not Leeds, Bradford or London good, but still good. Barbakhan on Walmgate is an amazing Polish restaurant. That street also has a good Argentinian steakhouse. Your friends won't go wrong with either Little Italy or Delrios for Italian.
Pubs / bars - your friends can take their pick really. I'd go to the Petergate, Goodramgate / Shambles areas for nice pubs (that is, the streets around the Minster). Lucia's on Swinegate is nice, as is the beer garden at the Lamb and Lion on High Petergate. City Screen, the independent cinema off Coney Street, has a really lovely cafe bar. That street and Micklegate should however be avoided on Friday and Saturday nights. The House of Trembling Madness, a bar on Stonegate, is good and is in an old mediaeval room (good bar snacks too).
For nice café's, there's a number on Bishopthorpe Road, just outside the city walls. Goji on Goodramgate is generally reckoned to be one of the best vegetarian friendly cafes. Friends are also having about a new Japanese tea room (don't know name).
For daytime, in town beyond the obvious museums and City walls, Barley Hall, an old mediaeval townhouse, and the Roman Baths museum (under a pub if the same name) are interesting little known historic places. Treasurers House is a NT house in the city centre. Out of town you have Castle Howard. I could go on...