Agree with Mark's list above. The catch though is that you've only three days, so the key thing is to prioritize. You could easily spend weeks doing nothing but visiting Museums in London and still only scratch the surface - I'd suggest perhaps taking a look at the museum web sites in advance, and pick just one (or two, if you're a big museum buff) that best reflects your interests.
Given the short amount of time, it might be worth taking a bus tour. I usually avoid these and tend to regard them as being 'touristy', preferring to see the main sights by foot and tube on my own terms, but they are a great way of getting a good overview of the city and at least checking off the main sights while getting your bearings. Do this early on your first day, and you can then decide what parts to fill in or concentrate on on your other days. Some of these bus companies basically run a fixed route in one direction and have guided commentary, and once you buy your ticket, you can use it for the rest of the day, hopping on or off at the various stops as you want.
Also consider getting a copy of Time Out London as soon as you land, it has good listings of what's on in all the museums and theaters with reviews. It will also list what live music and clubs nights are on, so can be a useful guide for figuring out which of the city's nightlife options will be most appealing to you. I think there's also a couple of free 'event guide' brochures available, though can't remember the names of them at the moment.
Also, think carefully about how to use day time vs evening time: a museum can easily eat up a hefty chunk of daytime, and by the time you're leaving, other daytime attractions will be closing for the evening. So if you're thinking of doing the London Eye, if you do it in the evening instead, it won't eat up otherwise valuable day time.
If you're in town on a Wednesday onwards, consider going to see a show in the West End. If you really want to see a specific show, perhaps book a ticket in advance, otherwise head to the TKTS discount ticket booth at the south end of Leicester Square in the morning and see what shows are going for later that evening.
Lines for something like the Tower of London can get quite long in peak tourist times, so check to see if they have a website that lets you book in advance, or make it the first thing you do on a specific day and get there early so you avoid spending too much of your day standing in line.
Also recommend checking out a pub or two; you'll find pubs scattered all over London, Time Out has a list of some historic ones here. Pubs are usually a lot cosier than US bars are, and usually have a different selection of beers on tap than you'll find in the US. Notable are the "real ales", which are pumped into a glass via hefty manual levers rather than the taps you see at most bars.