There is a Premier Inn (London County Hall) situated a few minute's walk away from the London Eye and Waterloo station. I have been there myself and can confirm that it's a nice hotel at a great price for a London visit.
If you're looking for areas in general then it depends on what you want to do. Of course the Tube and buses make it very easy to get to where you want to go, but to be close to the tourist areas then the West End is the place to be. This is where Oxford Street, Piccadilly Circus, Trafalgar Square and many other tourist attractions are.
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