Don't worry too much about the location, other than roughly central London (Zone 1 of the Metro), near a station, and some decent pubs nearby. The places you will probably want to see are scattered enough that you will be using buses or the underground. There are a number of Premier Inns that are always dependable comfortable rooms, perfect for a couple nights.
Rick Steves has a couple of good walks that can be combined to see most of London along the river (Westminster, St Pauls Area, and Southbank). The British Museum (free by the way) would be the top of my list (besides the stuff you can see walking around) then whatever is within your interests (Art: National Gallery or the Tate, History: Imperial War Museum or the Victoria and Albert, Tower of London, Westminster, etc.)