There are B&B’s in London, which may be cheaper than hotels. I know there are several in Kensington, which is a nice area and reasonably central.
Travel tips:
Buy a weekly Travelcard if you’re planning on spending most or all of the week in the London area. Zones 1-2 will cover most of the main tourist attractions in central London, and Travelcards are good for the Underground, trains, and buses (apart from the sightseeing buses).
Getting mugged is pretty unlikely, but pickpockets are common, so beware of placing anything valuable in outer pockets or open bags. Always watch your bags in public places – this means don’t drape purses over the backs of chairs, and such like. Basically, don’t put anything worth taking in a position to be taken.
Try to avoid using minicabs – get a black cab instead. If anyone asks you “You want a minicab?”, just say no – they’re not legally allowed to solicit anyhow, and while most will get you where you want to go in one piece, some … won’t.
And don’t eat at any of the steakhouses. They cater exclusively to tourists who don’t know any better, and their kitchens are often less than hygienic. I mean it.
Things to see: I’ll second both the Tate Modern and the London Eye (bring binoculars); plus, now that the wobbly Millennium Bridge is no longer wobbly you can walk straight over the river from the Tate to St. Paul’s (or vice versa). I dunno if anything will be on at The Globe (which is near the Tate Modern), but you might find that an interesting experience (helpful tip: dress for outdoors, and if you have a seat rent a cushion – your butt will thank you).
Pick up a Time Out magazine as soon as you get into town, and it will have details about what’s on and where. Concerts, plays, art exhibitions, club life, comedy shows, the whole nine yards.
Apart from the big museums, you might try the Sir John Soane’s Museum near Holborn station – an amazing house full to the rafters with stuff. All kinds of stuff, from a sarcophagus in the basement to paintings to bric-a-brac of all types. I also always recommend the book displays at the new British Library near St. Pancras station. If you’re even a mild bibliophile, this is worth a visit.
On the river itself is the HMS Belfast if you’re into big naval vessels; Tower Bridge is nearby, and there is a museum in the bridge itself (which, I understand, includes a walk across the upper span of the bridge).
Outside of the center (excuse me, “centre”), you might try Hampton Court Palace (about a half hour or so journey from Waterloo Station) and Kew Gardens (probably not all that nice in March, though, apart from the enclosed gardens).
That’s probably enough for now.
