Romantic: The Blue Bicycle, Fossgate is a York tradition for these sorts of occasions, serving French cuisine.
More relaxed: Melton's Too, Walmgate (there is a more formal Melton's on
Scarcroft Road). This time of year they should be doing seasonal menus, which means locally-grown asparagus. Very good prices, they also do tapas.
Vegetarian: Vanilla Black has moved to London, so try El Piano instead, especially if you can get a seat in one of the smaller upstairs rooms. Mexican and tapas.
Real Carnivore: There's an El Gaucho, an Argentinian steak-house on Walmgate as well, which will burn meat of all descriptions for you (yum!).
Indian: That's a toughie, the Himalayan on the Mount is (was?) pretty good, as was the Bengal Brasserie, but don't quote me on either of those as it's been a while.
Italian: L'Antiqua Locanda, Shambles (NOT Bari, opposite it). Fantastic Italian, not the usual Pizza Express/Ask 'popular Italian'. Excellent wine list.