Each time we stay in London, we try a different area. We stayed in Kensington just over a year ago and liked it. Not too far from museums, the park (you can walk through the parks to Haymarket, etc.) and shopping on Kensington High Street.

We stayed at The Vicarage Hotel, a Rick Steves' fav. It was off-season so we actually managed to get a room! http://www.londonvicaragehotel.com/ Very nice, good room, good breakfast. Convenient for transit. Beautiful gardens in Holland Park.

Frances Toronto, Canada