^^^Marriot County hall is nice (not sure if it fits your budget though?) There is also a Premier Inn at county hall which will fit your budget (they are cheap and cheerful like Holiday Inn, but perfectly good for the amount of time you'll spend in it!). County hall is right next to the London Eye and over looks The Palace of Westminster (Big Ben). You'll be within easy walking distance of Westminster Abbey and if you walk up Whitehall (just over the bridge) you'll go past Downing Street and be in Trafalgar Square. Plenty to keep you busy, plus you can get a boat from County Hall down to the O2 (and the Marriot is the players hotel for the event!). If you want to be nearer the 02, but still not on top of it the Guoman Tower at Tower Bridge is nice and there are plenty of restaurants around St Katherines Dock and Victoria Wharf over the bridge, plus really nice walks along the bank of the thames (again plenty to keep you busy!).
Hope that helps!