Down from Edinburgh for the day, are you mad? Stay for a weekend, here is a post I wrote a while back, I would still do the same thing if I was a first time visitor.
Parts of London are pretty trashy, you could spend a weekend in Leicester Square eating in Angus Steak Houses, going to M&M's World and spending time with other tourists or you could seek out some interesting things to do. Plenty of cheap or free things, the museums are great, lots of cheap, great food and loads of interesting night life.
Get an oyster card, stand on the right, wait for others to get off the tube before boarding and move down inside the carriage then maybe Londoners will hate you a little less.
Parts of London are pretty trashy, you could spend a weekend in Leicester Square eating in Angus Steak Houses, going to M&M's World and spending time with other tourists or you could seek out some interesting things to do. Plenty of cheap or free things, the museums are great, lots of cheap, great food and loads of interesting night life.
Get an oyster card, stand on the right, wait for others to get off the tube before boarding and move down inside the carriage then maybe Londoners will hate you a little less.
Here is a rough guide on what to do.
Assuming you arrive Friday, cocktails and dinner somewhere nice, Claridges and Wild Honey (need to book) are good, won't break the bank (~£60 a head ish) but are great, both are in Mayfair.
Saturday
Start in Trafalgar Square (National Gallery if that floats your boat), down the Mall to Buckingham Palace, down to Parliament Square, see Westminster etc. (optional run across the river for a trip on the London Eye at this stage, its just over the bridge from Westminster), up Whitehall and see Downing Street, back up to Trafalgar Square and on to Covent Garden.
Lunch in Covent Garden (Wahaca is nice), from there through Leicester Square, to Picadilly Circus, up Regent Street (shopping), across Oxford Street (shopping) and down Bond Street (more shoppng...) then maybe tea at the Wolseley (advanced booking a must), along Piccadilly and back to Piccadilly Circus. Try http://www.insider-london.co.uk/ walking tours if your not the shopping and tea type.
Back to the hotel, ****, shower and shave, and get back out.
Cocktails somewhere before dinner, head to Soho for a good night out. Mark's Bar (in Soho) is a fave, dinner somewhere after, Bocca Di Lupo (Italian in Soho which you need to book well in advance) is good, ask to sit at the bar in front of the chefs for a little dinner theatre. After this hit up some Soho bars, try Graphic, Floridita or the Experimental Cocktail Club.
Sunday
Start at the Tower of London, will take most of the morning (2-3 hours depending on how keen you are), then across Tower Bridge and down to have lunch at Jose or Zucca (need to book either!). After this if you absolutley must do the dungeons your only 5-10 minutes walk from them, I wouldn't bother but if you keen then go ahead. I would much rather take a short cab ride to Brick Lane Market, great buzz and a real bit of London.
This lot sounds a little mad, but trust me, its a sensible route (all the stuff is walkable unless noted and in a clear order), taking in the best of London, bit of tourist stuff and a bit of real London. I wouldn't bother with Madame Tussauds or the Dungeons, the are real tourist dumps, are expensive and you will queue for something that's not worth it.
If you want to skip the Eye (its ok, not much to write home about) go to Paramount, a bar (and restaurant) on the 32nd and 33rd floor of a building called Centre Point next to Tottenham Court tube, amazing 360 degree view, you can spend as long as you want up there and have nice drinks.
Anyway, have a think about all of this, I can't think of much else I would want to do on a weekend.