Chef's Table/Wine Cellar
We've always enjoyed going to Compass, and I think Chef John Fraser's New American cuisine is excellent. The have several private dining spaces, one of which is a Wine Room. A chef's table usually involves being in or very near the kitchen and having the chef cook especially for you. I don't think Compass offers that.
We had one meal at Philip Marie many years ago (not in the private space), and I thought the food was decidely ordinary.
Since you don't indicate any budgetary restrictions, you might want to investigate Daniel. I think they may offer a Chef's Table.
Country, in the Carlton Hotel, may also have a Chef's Table.