That's a great location, close to pretty much everything. What surprised me in London was how many things were actually within easy walking distance and didn't even require the use of the subway (by the way, call it "Underground". In addition, the centre of the city is full of helpful maps for tourists, on just about every street corner, so I rarely even had to bother taking out my city map. Although the subway is amazing - waiting times are extremely short, prices reasonable and it's always busy enough that you never feel unsafe even at night, but on peak hours you'll want to avoid the central-London stations as I understand things can get extremely crowded (guess I got lucky and avoided that myself).

And then there's the issue of the roof of one of the London theatres caving in just a month or so ago...

The musicals playing in London are indeed likely to be mostly the same ones as on Broadway - for someone from any other city in the world than New York it would be on the list of things to do in London, but well, yeah. I had intended to go see The Mousetrap, a play based on an Agatha Christie detective novel that holds the world record for longest-running play at over sixty years and 25 000 performances, but didn't get around to it. So no idea if it's worth it.

If you don't much like museums, one of London's best features are arguably its parks, weather permitting (which I suppose it might not do, in January). Hampstead Heath up north and Greenwich Park in the south are both lovely, and then there are a bunch more in the centre. The open-air (mostly) markets of Camden are quite fun if you like shopping for clothes, decorative items, music, books, and quite a lot of other stuff. Foley's on Charing Cross is the big independent bookstore, think London's counterpart to The Strand.

You could always go on the London Eye, the huge ferris wheel with great sights of the city, but then on the other hand the price is ridiculous and the queues impressive, so there are better places to go see the view, such as the Monument (a monument for the victims of the Great Fire of London in 1666, a very narrow tower of about 200 feet high), or the hill in Hampstead Heath.

If your dislike of museums doesn't extend to historical buildings, you definitely can't miss the Tower, and I guess St. Paul's is also well worth a visit - though both are expensive. Museums and similar attractions in London are either free (though donations are recommended) or absurdly expensive, there doesn't seem to be a middle ground.

As for eating out and going out, you'll be in a great neighbourhood for that, but as Tom mentioned, the ridiculous closing hour at 11 pm for British pubs (not all of them, but most - clubs will stay open longer if you're into that) does put a bit of a damper on things. I didn't find the prices for food too unreasonable (alcohol was more expensive though), but then again I'm used to euros and found American prices pleasantly cheap even last time I was in the States - and by now the dollar has eroded further.