Hi.
I was there before Thanksgiving. I used an American Airline package that was cheap; $1000 for 4 nights and air fare. We stayed at the Millenium Knightsbridge, which is a fantastic location, close to tube, Knightsbridge. London is very safe, so you should be fine. We bought a week tube pass and took the tube to and from Heathrow. Be aware; when you leave London at Heathrow, you can have only 1 bag!
Marcia