If you're doing museums don't forget the
Leonardo Da Vinci exhibition at the National Gallery, and as Damian says tea at The Ritz is fun, but you have to book ages in advance.
You could then wander through Burlington Arcade into Bond Street and work your way up to Liberty - my favourite shop in London. When you're all shopped out, jump in a cab & head for Marcus Wareing's restaurant at The Berkeley Hotel. Well that's what I do every now and then
We Londoners are notorious for not doing the touristy things on our doorstep, but the London Eye is worth a spin if you squeeze it in!