Right.
My recommendations...
Well, IF the sky is clear, I dunno, the London Eye is amazing, but somehow, standing in the middle of Waterloo Bridge, on a clear clear - well I was there at night - just took my breath away. I couldn't believe what an amazing city I now live in.
LOADS to do for FREE - but you didn't state what you're particularly interested in; walking tours, on your own, theatre, museums, etc.
Always something new to find at the British Museum, as well as old friends to go visit
. I love that I work right down the street, and I get to say I went there on my lunch hour... and right now they have a very cool Mummy exhibit, that has a narration by Ian McKellan (there's a charge for that, but to wander around the museum is free).
My personal favorite, The National Portrait Gallery. Again, always something new to see... and always more to learn about the monarchy, history, people, etc.
And right around the corner, The National Gallery.
And as Britwife mentioned, St. Martins is right there as well.
Take in the awe of Trafalgar Square, the Lions, and Maj. Nelson
If you're interested in legal history, the Inns of Court is just around the corner on The Strand.
Aimlessly wander around Covent Garden - The London Transport Museum and Shop is very cool, and full of interesting gifts....
I'm sure I'll think of more, but hopefully that will suffice for now