We were here at Christmas, and enjoyed our meal at The Audley, a traditional pub at the corner of Mount St. and S. Audley Street. You can either eat in the downstairs bar or upstairs in the restaurant.
We also enjoyed our Christmas Day dinner at Ozer, one of the Sofra restaurants which specialize in Turkish food.
http://sokfra.co.uk I believe that there is also another of their restaurants closer to the hotel.
My 13yo loved Wagamama, a fun noodle restaurant at the other end of the square, about 2 blocks away.
http://wagamama.com
Hope that helps...