Ditch the Lonely Planet guide... (Score 1)

Like all major cities, London changes too quickly for guide books to keep up. Here are a few things (some mentioned previously) that are more fun that doing the conventional tourist trail around London...

Leave the laptop in the safe at the hotel. Take your camera instead, spare batteries, and a spare memory card. Look up - lots of interesting details above eye level.

Food:
Borough Market (London Bridge on Thu/Fri/Sat/Sun, fantastic, fun food market with lots to see)
Whole Foods Market (High St Kensington or Clapham Junction if you're homesick)
Eat a pre-theatre dinner, or have lunch, at a really good restaurant. You'll get 2 or 3 courses for under 25 GBP, for the same food that costs three times as much in the evening.

Pubs:
The George (Borough or London Bridge)
Lamb & Flag (Covent Garden or Leicester Square)
Any Sam Smith's pubs in central London (The Champion - stunning original pub interior - on Wells St just off Oxford St, Red Lion on Kingly St, The Angel by Denmark St, The John Snow, )

Drinks:
Drink a pint of bitter, just once at least!
Two good London breweries are Fuller's and Young's.
Fuller's London Pride is a decent bitter.

Things to do:
Spitalfields Market and Brick Lane (beautiful architecture, Georgian townhouses, Hawksmoor church, hip street market on Sunday and lots of hip, cutting edge/retro clothing/culture)
Walk around the hip Rivington Street area / Shoreditch (this area was discovered by 90s geeks - it was the original centre of the UK's New Media industry)
Walk around Mayfair (pretty, expensive, villagey residential area above Oxford St)
Walk around Covent Garden (see the Georgian Market, fun shopping area)
Broadway Market (old, now very hip East End weekend market Sat/Sun)
Walk along the South Bank between Waterloo and London Bridge at night
Go to a West End show, either theatre or musical, or The Globe for Shakespeare
Go to a gig: London has a fantastic and diverse music scene
See an art show
Highgate Cemetary (incredibly atmospheric and ancient, great for photos, try to get onto the old cemetary tour)
Sample sales. London's a key fashion city. If you like shopping for clothes, shoes, accessories etc, go to a sample sale. Usually 3-4 weekly somewhere central. Fun, hectic and great discounts.

Other museums:
National Gallery (free, incredible collection)
Courtauld Institute
Royal Academy (usually has good shows)
Tate Britain (lovely building, good collection, great cafe and restaurant too)

Destinations around 1hr from London:
Oxford (Bodleian Library)
Brighton (Pretty, classic British seaside town)
Canterbury (stunning World Heritage city, 10th century cathedral and original 16th century quarter)