I have been researching hotels in London for my upcoming vacation in Sep ( yes, I like to plan way in advance

) and already have read thru some of the threads in this forum and browse thru the websites of many London hotels. The choice as expected is quite bewildering, but none really impresses me enough to book so far.
As it is my first trip to London, I am looking for location as paramount ( must be convenient and preferably walking distance to all the tourist place ) and near subway which I presume should be everywhere in London as in any modern big city. I'm not familiar with London at all and I have heard that Hyde Park, Knightsbridge and Mayfair and places around there are all good locations ( Am I right? ). Next will be comfort and modern amenities. Size is also important ( 30m2 min or larger ) as strangely, I see luxury hotels in London tauting what I will consider as shoe-box size hotel rooms at 25m2 or smaller and called them "deluxe" rooms. And also quiet with good sound-proofing as I'm a light sleeper. I won't really care too much about ambience or restaurants or excellent service ( but can't be too shabby too! ) as most of my time I will be outside sightseeing or visiting friends. Budget preferably within GBP300 per day or less but willing to pay more for better quality and/or more comfortable/spacious rooms.
I have shortlisted these based just on recommendations from some of you and also after checking out their websites. This is my list ( not in order of preference ) :
1) Connaught
2) The Mayfair London
3) The Aldwych
4) Sheraton Park Tower
5) Knightsbridge hotel
6) SOHO hotel ( #1 London hotel in tripadvisor but location??? )
7) The Halkin
Will appreciate any comments and feedback that you have esp if you have stayed at some of the abovementioned hotel. Thanks in advance!