I have lived here for fifteen years, and would strongly recommend dining at La Bouchee, my favourite local brasserie; reservations are recommended:

56 Old Brompton Road, London, SW7 3DY Map
Nearest Tube Stations: South Kensington - 286m Gloucester Road - 396m
Telephone: 020 7589 1929
http://www.london-eating.co.uk/2492.htm

It's a little bit of Paris in the heart of London.

I would also recommend Le Colombier, a short walk down the road.
145 Dovehouse Street, London, SW3 6LB Map
Nearest Tube Stations: South Kensington - 522m Gloucester Road - 861m
Telephone: 020 7351 1155
http://www.london-eating.co.uk/1646.htm

Both are stalwarts, places I go when I want consistently good service, excellent food and a relaxed stress free evening out.

I can also recommend my latest find, the jockey Frankie Dettori's restaurant family focussed restaurant, "Frankie's" Frankie's Italian Bar and Grill 3 Yeomans Row, Phone: 0207.590.9999. which is quite close to Harrods. Best deluxe burger in twon.

If you want super high end then L'Aubergine is probably the best near to your hotel, but prepare to take out a mortgage if you would like to dine there, especially given the weakness of the dollar.

Have a great stay and PM me if you need any other suggestions.