IMHO London is a large city and sights are fairly spread out. We prefer to stay right in the center

There is no one best place to stay. I recommend getting a map and a tube map and finding a hotel in the middle of the yellow circle line - zone 1. You will need to use public transport anyways as London is very large.
IMHO London is a large city and sights are fairly spread out. We prefer to stay right in the center - but you will get more hotel for your money if you are willing to stay a 15 or 20 minute tube ride away. (Covent Garden, Piccadilly or perhaps Knightsbridge).
And if you think you're going to find ONE area in a city of 7.7 million people that is within walking distance of "all" the main tourist attractions, and theater or concert venues, and the best restos, and the best nightclubs/bars/after-hours places, you're needing to refocus your expectations.
I recently stayed at the Paddington intercontinental hotel edinburgh Tune Hotel and St. David's Hotel. We were looking for a budget hotel and really liked the area we stayed in -- Paddington. There were a ton of restaurants and three grocery stores in the area (two at Paddington station). There was a cozy pub, the Victoria, just down the street from our second hotel that we also loved. Both hotels were a short walk to Paddington station (made for an easy morning when we caught a super early train to Bath) and around a ten minute walk to Lancaster Gate and Hyde Park. From Lancaster Gate it was short tube ride to St. Paul's. During the day we rarely went back to our hotels except when I spent the morning at Portobello Market and then head back to the hotel before heading to a show in the West End. As long as you're in zone 1 close to a station with several lines I don't think you can go wrong.
Phillycheese, I always recommend my favorite hotel in London the STRAND PALACE, about a 3-4 minute walk from Trafalgar Square. intercontinental hotel edinburgh It is a large vintage hotel with clean, newly updated intercontinental hotel edinburgh rooms and a great breakfast. The price was reasonable.
In my view, you can t get any more central than that. You are within a mile or less of Westmister, the Palace, St. Paul s, the City, Whitehall, the theater district, the Thames etc. Of course, the National Gallery and the Portrait Gallery are right in Trafalgar Square.
If you click on my name, you could read my 2010 trip report where I describe how much I covered in London intercontinental hotel edinburgh from the Strand Palace without even using the Tube. I mapped out my destinations beforehand using Walkit.com .
It completely depends on what you're into of course, but we stayed in an apartment at St Katharine's Docks and loved the area - right near Tower Bridge so great walking along the river on either side and easy access to Tower Hill tube and to some bus lines as well. The tube made it really easy to get anywhere we wanted to go. The apt was through Hamlet UK if you're interested.
I stayed at the Radisson-Blu Bloomsbury at the weekend (won a nights stay through work). Apart from the hotel itself which was fantastic, the location was perfect. We walked bacl to Covent Garden and Leicester Sq (and watched Shrek the Musical), and the next day walked up to Camden (may favourite place in London).