Unless there’s something specific you want to see, just walk around. Walk down the river. Start at Lambeth Bridge, across from The Houses of Parliament, head towards The London Eye and just keep walking. You’ll see loads. Or like Karina said, take the boat down to Greenwich and you’ll see everything. The old and the new. I’d avoid the museums and art galleries because they’ll be absolutely packed and you’ll barely be able to move let alone see anything. I know London seems huge, but it isn’t really. If you start at Trafalgar Square you have Covent Garden a few minutes walk away in one direction, or The Mall and Buckingham Palace in the other. Or you can walk up The Strand onto Fleet Street and you’ll come to St Paul’s and The City beyond. You can easily walk up to Piccadilly Circus from Trafalgar Square too. The tourist buses sound like a good idea. Using the Tube is great if you want to get to a specific place, but I always think you never see anything when you’re under ground.