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.

London is the most interesting and lively city in the universe I know, so it offers too much to mention. As a tourist I recommend the hop-on hop-off bus tours. You can combine driving in one of the old red buses, listen in your native language to informative and interesting tales about the places and houses you see, no crowd among you and the tours can be quite comprehensive if you want. Also you can hop off where you like and have a walk. When you didn't walk through London for a while on your own feet you haven't seen it. When you are not adventureous and do not want to walk through Soho or Covent Garden then I highly reccomend a walk on the southbank from Big Ben crossing the Thames on the bridge and walking eastwards following the river seeing such marvels as the London Eye, The modern Mayor of London Office, old ship building yards that today are galleries, Albert Hall and always on the opposite side of the river the building of MI6, St.Pauls and numerous other things and buildings, it can be a long walk there until it ends at a small dock where a replica of Shakeaspeare's theatre has been built and a wooden replica of The Golden Hind, the ship of Sir Francis Drake. And do not forget to visit Ed's Diner in Soho an stroll from there to China town. When you like modern Architecture then there is plenty to see,the gurkin, the shard and St.Mary's Dock and the Millenium Bridge. Have a stroll through Hyde park or any other park. London is the most park rich city. Drive with the tube! That is where you can watch the locals. They are an international mixture from the entire Commonwealth. That might get you in touch with the people, literally but not on purpose. Beware: Pickpockets in the trains and stations are not as rare as you would want. Do yourself a favour and try not to pack your day with too many schedules. When you like that sort of thing this will be the sort of thing you like. And you likely return.