I recently stayed at the Grosvenor square Marriot. Very nice and your girlfriend will be impressed. Its not cheap.....if you have points, use them! It is within a couple of blocks of Purdey, William and Son and Boss. There is a tube station close as is shopping for her.
Take the "Big Bus" hop on, hop off tour first to get your bearings. Then go back to what interests you. The British Museum is pretty neat as is the Museum of London. There are several pubs very close to the Marriot and Chef Gordon Ramsey has a restuarant in the hotel. I thought London food sucked in general.