Camden is pretty much the place to go for the market, etc. Great for gay Gothic clothes and other such useful items. It's fully open on Saturdays and Sundays. Watch out for the Somali kids hanging around the Tube station though, and never buy drugs from anyone in that area if that's your thing. The place is constantly monitored and it's more likely that you'll be busted than the dealer (the local police are hitting "drug tourists" hard). There's a decent pub in Camden called The Devonshire Arms (ask a Goth where it is) which is strictly Gothic / Metal only. If you don't look the part then you won't be allowed in, but it's got decent music most nights.
Denmark street is still the place to go for musical stuff, with the Turnkey Soundhouse around the corner on Charing Cross Road being the Mecca for most. There's also a pretty huge musical shop in the basement of the Virgin Megastore (at the corner of Oxford Street and Tottenham Court Road). the prices are outrageously high, but all the equipment is very "hands on" if you want to try something out.
The London Dungeon's great fun, but the queues can be very shitty. Try and book in advance if that's possible. For free things to do you could try the great museums (British Museum in Bloomsbury, the Natural History museum in South Kensington), but each place would take half a day at least.
For something a bit out of the way, Hampton Court Palace is very nice (just 5 minutes from where I live). A train to there takes 30 minutes from Waterloo station, but it's worth it. There's also Richmond Park, but if you're not driving that could be a pain in the arse.
Buy an Oyster Card for the tube/buses as soon as you get to London. You'll save a lot of money that way rather than buying individual tickets all the time. Oh, and don't be ripped off by these tourist "open top" buses. The 15 and 23 buses go exactly the same route, but they charge £1.00 and not £15.00..
For Metal related stuff this website is pretty good:
http://www.metaltravelguide.com/php/region.php?regionid=14
Lee
