Hi I used to live not far away from the finish! Areas I would consider include:
Eccleston Square/Hugh Street/St George's Drive - you'll pay around £120+ a night here and its not as nasty as other parts of Victoria can be for hotels!
Further down in Pimlico is a days inn which is worth a look but I cant remember which road it is on. Its basic though.
Picadilly - you'll pay more for a hotel around here, but it is very close and you wont have to walk around the course to get back
County Hall/Waterloo way - you can cross the river at the footbridge and its about the same price as Eccleston Sq here
Or if you want cheap look at something like Earls Court and tube from Victoria which isnt far from the Mall either, but everyone will be going that way.
Its a pricey part of London - if you truely want to be within waking distance these two places are lovely:
Le Meriden - Piccadilly
Crown Plaza on Buckingham Gate