Jockbod48 saidMayfair and Knightsbridge, South Kensington and Hyde Park are my favorite areas of London.
Same here. I cannot say any of them are 'gay, artsy or odd', but they are definitely worth seeing. London is a great walking city, so get your walking shoes on and go. Instead of walking along trashy and overcrowded Oxford Street, walk along Park Lane, into Grosvenor Square (home of the US Embassy) and walk east through Mayfair, which is generally quiet (especially at the weekend) but full of great architecture and garden squares.
The City of London (i.e. the ancient square mile) of the city is worth exploring. The weekend is the best time to get around there, as the population drops from 300,000, to just 8000. There are many high rise buildings there, so it is not always easy to orientate yourself, but it is full of Wren churches and other historic buildings in the back streets.
I would also highly recommend walking the Thames Path from Albert Bridge in Chelsea to Tower Bridge. It is a 6 mile walk, but you are barely conscious of the distance, as you will see central London’s most famous sights along the way.