LOL!
Just as soon as I saw the heading, I could literally feel all my countrymen desperate to start teasing - it was just too good an opportunity!
Some advice, Oxford/Cambridge very nice but LOTS to do in London....
West End mentioned previously and I agree 100%. Check out Oxford Street/Marble Arch (don't bother with buses, too slow just walk) and Soho/Carnaby Street. Regent Street (off of Oxford Street) good for high end shopping, Tottenham Court Road (at end of Ox St, other end to Marble Arch) is good for tech, though not nearly as popular now because internet often cheaper. Covent Garden also good, but very touristy. Piccadilly Circus/Leicester Square not as found of, these VERY touristy and you also get all the chavs (don’t worry, you’ll learn this word when you visit!) coming down on night out from suburbs. TIP: DO NOT EVER miss-pronounce Leicester Square as ‘Lie-chester’. It is pronounced ‘Lest-er’ – you WILL intensely annoy any Brits in earshot if you do this.
Learn the tube (underground train network) – best way to get around on a budget. DO NOT strike up conversations with people on public transport – you WILL píss them off doing that.
Do not refer to anyone Scottish you meet as ‘English’ – that’s a good way to get punched in the face. Check out The Tate. Avoid South London. Try not to confuse speaking and shouting – the American voice/accent does have a tendency to, ahem, ‘carry’ shall we say.
Check out ‘toptable.com’ for good restaurants in London. Make sure you have a curry at least once here – Brick Lane is good (a little way out from West End area, but more authentic).
Above all, the best advise I can offer (through also the hardest to quantify!) is just try to not be too annoying. I hate to break it to you, but recognise that American tourists don’t exactly have the best rep in London, or indeed the, em, rest of world..