Saturday walk-in anniversary dinner

My husband and I have planned a last minute fifth anniversary trip to NY for the night. We don't want our day to be constrained by reservations, but still want a good meal. Not necessarily fancy, but something exciting and a good culinary experience. We like great food in a not too stuffy or pretentious atmosphere. We are happy to sit at the bar at a place we otherwise wouldn't get a reservation at this late date.
We're staying at 53nd and Madison, but are up for traveling (more likely to go downtown than up).
Thanks for your suggestions!