I've been a fan of Gramercy Tavern for a long time, and despite what you may think, you can afford to go there. Their tavern room (the front room where the bar is) is a no reservations space, with an abbreviated, but still excellent menu. From the $23 fillet mignon to an assortment of other dishes that change seasonally, all their food is flawless. Additionally, they do a wonderful cheese plate (you choose the number and type of cheeses) and charming, comfortable desserts. They also have a stunning wine list and a strong selection of beers and ciders, as well as liquors and after dinner drinks.
Most notable about Gramercy Tavern, though, is the service -- extraordinarily attentive, never intrusive and never oppressively formal, you almost don't notice your waiter is there. I've eaten here dozens of times and no one has ever been snooty with me, gotten an order wrong, or otherwise done anything to make me want to tip less than 20% (or more).
The Tavern room is suitable for romantic occasions, as well as friendly, family or business gatherings. It's also especially pleasant for lunch. And while it seems unnecessary to say in New York in 2006, they've always been extremely gay friendly to me and mine.
Additionally, I have also dined alone here several times, and have always found pleasant conversation at the bar, both with the bartender and other solo diners.