I've eaten solo at Tonys, Liberty Tree Tavern, Coral Reef, and Chefs De France. At each of these restaurants, I was treated better than when I went with my family! The only one I had a reservation for was Chefs De France. The rest were last minute decisions. This was last October, I think. I had to wait at Liberty Tree--for about 45 minutes. They told me that immediately, so I went off and did something else for a while. When I went back, I was seated immediately.
If you're not too fussy about the times you eat, you should be o.k. without reservations. I would imagine you'll have problems getting into CRT and LeCellier.
Have fun! We'll be there starting January 24. Can't wait!