I’m heading to London (birthday gift from my sister - how fookin’ cool is she??) during February. My sister is coming along but will be in meetings during the day. This means I get to tromp around the city and explore throughout the day on my own.
I know there are a million places to see and I really do want to hit the big ones. I’ll get a guide book and my sister will fill me in on a lot of the things but what about some of the smaller cool things you’ve found?
Tibs
I only live about 40 miles outside London, but still consider myself a tourist when I go there. Feb is a good time to be a tourist since the crowds are far smaller. How much time to you have? Some of the big attractions like the Tower of London and the British Museum can eat up a whole day or more. The guide I use is the Penguin London Mapguide (isbn 0-14-046954-0). It has short descriptions of the museums and attractions, and is a very easy to follow map. A good way to see alot without alot of walking is to get on one of the red ‘hop-on hop-off’ tour buses. They go all around the city and if you see something you like, get off and have a look, then get on the next one that comes by. Many times I just wander aimlessly thru the city and when I get lost I just find a pub, have a pint, and look at the map. On a good day, I may get 5 pints worth of lost!
Take at least a whole day and do the British Museum (properly done it would take longer but you’re doing the tourist thing). The BM is outstanding and last time I looked it was still free (donations accepted, however).
If you’re indeed doing the tourist thing, you may as well hit the Tower. The warders there are usually great and it is expected of us tourists.
Depends what you’re into. If you want to cite some interests/tastes, I can give you more specifics.
First thing I’d do, if I were you, would be to buy a ‘Time Out’, go sit in a pub, have a drink, and browse TO for ideas. Then it’s down to you, your tube map and your Weekly Travelcard (much better than any alternative way of getting around).
Do check out the ‘London Walks’ which are listed in TO. All very good, cheap, fun, informative and interesting.
All the big art galleries, museums… yep, fine if you like that sort of thing. National Portrait Gallery and Tate Modern both worth a look. Science Museum and Natural History Museum both personal favourites, but YMMV.
Sight-seeing tours on top of red double-decker buses: usually very good and enjoyable, and good for getting more ideas.
London Eye (big Ferris Wheel kind of thing put up as part of Millenium Celebrations): fantastic, worth doing, but can be a bitch to get tickets. Can provide more details if you’re interested.
Hampton Court Palace: if you haven’t been, GO. Easy as that. Spend a day there. Beautiful, fascinating, pleasant, evocative.
Buck Palace: ardent Royalists only. Otherwise boring. Nothing to see.
Westminster Abbey: stunning. Go. More history than any one person can absorb! Not to be confused with Westminster Cathedral, which is not so hot.
Booze: cheapest way is buy from supermarkets and consume at your leisure. London pubs are frighteningly expensive.
Food: over here, Indian food is GOOD. Enjoy it while you can. Cite your preferences, and I’ll offer recommendations.
Hyde Park: biggest and best we got. Dead central, safe, easy to enjoy. Shame it’s February, 'cos weather won’t be nice.
Entertainment: London scores highly here except for movies which you’ll already have seen. Comedy, rock, jazz, theatre, musicals, dance, clubs… tons of it in endless supply and quality is high. Again, if you want to cite tastes I can recommend some ideas.
Greenwich: nice place to visit on a weekend morning. Treat yourself and go to the Pie & Mash Shop.
Soho: some great places to hang out, drink ,eat, chat. Worth just schmoozing around and seeing what you find.
Kensington & Chelsea: the high-class end of town, posh shops and big-name stores selling cool stuff you can’t afford. Fun to visit, though.
Richmond Park: vast, wild, wonderful. If you want nature, this is your best shot within the Greater London area.
Camden Town & the Camden market: go if you haven’t been already, on a Saturday if you like crowds! Home for the street-smart, hip, counter-culture crowd with the most amazing (and vast) market selling everything. Most of it legal.
Portobello Road: antiques paradise.
I could go on, but I won’t. Do yourself a favour. To avoid disappointment, EXPECT lousy weather, litter, frightening expense, generally lousy service in shops, and transport difficulties. Once you are prepared for these, you can enjoy all the GOOD things the city has to offer.
Rule 1: never buy anything ‘edible’ from a cart in the street, unless feeling suicidal.
Rule 2: learn the name and location of at least one nice pub in central-ish London. Armed with this information, anyone in the city can find you or meet up with you. That’s how we natives organise our social lives.
Rule 3: mind your wallet or purse VERY carefully. These get stolen at the rate of 100 a second. It’s a serous problem. Safest option: carry only essential credit cards and cash. Wear jeans or trousers, keep them in a front pocket. Carry a decoy purse /wallet with nothing valuable in.
Welcome!
Looks like everyone has given you good information. I’d just like to add that if you like fish, please don’t leave London without going to a fish and chips place. Not a fancy place, just a little hole in the wall place. I would give my left earlobe to have some of it right now. 
Best time I had in London was in Parliament, Westminster Palace.
Mrs. RickJay and I went there with her family and one evening they were driving us nuts so we went back downtown without them. At about 8 PM we’re walking by looking at the statue of Cromwell when Mrs. RickJay notices some cops standing around one of the entrances. “Maybe they’ll let us in to look around,” she says.
“Sure!” they say. “Come right in!”
We toured the whole place, saw the House of Commons and House of Lords, with nary another tourist in sight. It was awesome.
Good fish and chips can be had all over London but I really liked Shakespeare’s, a touristy little place just across from Victoria Station.
This a big one, but don’t miss it: The Tower of London is fantastic, and make sure you go on the Tour. The Beefeater tour guides are hysterical (I’m sure it’s a scripted schtick but it didn’t matter). My friend and I went with the intention of just ducking in, seeing the crown jewels and leaving. I’m glad we didn’t.
Also, as much as I hate books with this sort of title, “The Idiot’s Guide to London” has great maps, very detailed directions and a number of good tour routes.
Fenris
Others have already hit the high spots, I’ll just log a few personal preferences:
Museums – the BM has plundered the best from all over the world. Don’t miss it if you have any interest in archaeology. The Tate is great for interesting pigments arranged in frames.
Theatre – go. Go often. Go some more. Braodway quality (or better, IMO) shows at half the price (or less). Cheap tickets often available at short notice, too.
Food – eat Indian, eat Chinese, eat damn near anything except mushy peas. The British founded an empire based upon the quest for a decent meal. Personally, I would forgo fish & chips ebtirely, but the chips do show off the one true British contribution to world cuisine: vinegar on chips. mmmmmmm.
Booze – drink bitters, drink stouts, drink ales, but stay away from the pils.
Mind the gap.