Hi--we stayed at Sloane Gardens in February of 2007. We had two apartments, a 1br and a 2br, through SFX, because we brought our three children. It was a GREAT trade. I worked for a British company for many years and Sloane Gardens was by far the nicest place I ever stayed in London.
The building is about half a block from the Sloane Square tube station. There is a bus about half a block in the other direction that is the best "tourist" bus in the London system. It goes direct from Sloane Square to Harrod's, to Trafalgar Square and Westminster Abbey and the West End and the National Gallery and most of the sites that you would like to see. We bought Oyster Cards at the tube station. The decision-making process for the transportation seems very complicated, but really you just go down to the tube station on your first day and buy one-week Oyster Cards and you're good to go.
I know London fairly well (from all those years of working for a London-based company), so we didn't do any of the hop-on, hop-off tours; we just decided where we wanted to take the kids and then we went. The dollar was so weak that we really felt we had to save some money where we could.
When you arrive at Sloane Gardens, there is a "greeter" named Joseph who checks you in and helps you get settled. He can answer questions about transportation and things to see. He's also at his desk in the lobby in the mornings.
Is there anything I can help you with about London? Are you planning to go to the theater? My DH is a big theater buff and will have lots of advice for you!
Oh, the weather--I've been in London for Thanksgiving before. The days are very, very short; I think it gets dark about 4:00 in the afternoon. But the weather in London is milder than in NYC and it doesn't get bitingly cold the way it does here. Here's a chart. I was going to say the days are in the 50s and the nights in the 30s, and that's about what this predicts.
http://www.weather.com/outlook/travel/businesstraveler/monthly/UKXX0085?from=36hr_topnav_business
HTH! Let me know if there's anything else I can tell you.