Can't speak to hotel points, but I would strongly suggest not Paddington. It's not a nice area, or an interesting area, at the best of times and the construction work going on there at the moment renders it even less nice.

With such a short amount of time, you should stay centrally. Go straight to the hotel, dump bags, go out to dinner. Crash, then go straight from hotel to sightseeing after breakfast. Return to collect bags before heading to airport. So your hotel needs to be where you will be sightseeing. The question is, where is that?

If it's the standard stuff, you need to be as close as possible to Westminster, or Trafalgar Square / The Strand. This will take in Houses of Parliament, London Eye, Buckhingham Palace, National Gallery, The Mall, Horseguards, Churchill War Rooms, Covent Garden and pretty well all the "signature" sights. If you are particularly interested in something, however, you might vary that by your interest (for example, modern art, might lead you to stay further east near the Tate Modern, or military history, might lead you to stay further south near the Imperial War Museum etc.).