I have stayed at Harrington Court apartments several times in the last six months and really recommend them for location, cleanliness and overall value.
The apartments are rated 4 star and the furnishings and decor are all contemporary. I have stayed in Studio and One Bedroom apartments but was upgraded once to a Two Bedroom, which has 2 bathrooms and really a lot of space for central London. Whichever apartment I have stayed in has been exceptionally clean - and I have stayed in a lot of places - and the service very good. Daily housekeeping is part of the deal and, of course, you have a full kitchen and dining.
Harrington Court apartments are 1 minute from South Kensington tube station and buses also go from very close by. Natural History Museum, Science Museum, VandA Museum, Kensington Palace and Gardens, High Street Kensington etc. are all an easy walk and other sights are rerally easy by tube - mostly direct. From Heathrow, the tube comes direct to South Kensington.