In London I always recommend avoiding the junk like Madame Tussauds and instead seeing interesting stuff like the Cabinet War Rooms as it's a unique place and extremely well set up, but it depends if you have any interest in WWII
The Tate is better than the National Gallery if art is what you want.
The British Museum is great too, but it's ridiculously big so well worth working out what you want to look at in there before you go - I like the weird obscure stuff like Dr John Dee's alchemical instruments (seen one mummy, seen 'em all...). The pub opposite the main gates, The Museum, is where Karl Marx used to have a beer (less tourists in an evening). I personally liked The Sun on Drury Lane, as it's more of a back street boozer and where Oliver Reed used to drink
Pubs in London are generally one of the best things about the place. Good pubs in Soho too. Otherwise I'd say make sure you get up to York as it's way more interesting and picturesque (it also has hundreds of pubs of course...).
Beer:
http://fancyapint.com/index.html
http://www.beerintheevening.com/pubs...county/London/
http://www.randompubfinder.com/
http://www.london-drinking.com/