The LA board had a great thread about this--NYC has at least one place that's canine-friendly on the UES. The Barking Dog Cafe, which had fresh, well-dressed salads and sandwiches (especially for the area-- 1678 3rd Ave, 212-831-1800)in the $7-10 range, has been around for a long time but doesn't seem to have shown up on these boards. There's a place where dogs can drink and the waiters' tea shirts suggest you "Sit" and "Stay."
I'm pretty sure there's at least one place downtown in the West Village. Is it still there?