there is one of these hop on/hop off tour bus companies that's a good way to get a nice overview of London.
It's called the Big Bus Company. They have open-topped double decker buses (the top is open so you have a good view.) They also have live guides giving you a play by play of what you're going by.
They also include several walking tours in the price of the 2 day ticket. I went on two of the walking tours and they were great (the ghost and pubs at night and the morning changing of the guard tour - both were EXCELLENT).
Their URL is
http://www.bigbus.co.uk/
I would ride around on them once to get an overview and then use them as a hop on/hop off if you like.
Go to their website and download the map of London with their tour route on it to help in your planning.
That URL is
http://www.bigbus.co.uk/uk/html/i/WinterLondon_Map2005_041005.pdf
I just looked at the map. The main route is the Red line route - that's the one with the live commentary and where the main "tourist attractions" are.
Another great tour guide company is called London Walks. They have walking tours as you can tell from the name.
Since London is a town that it's best to see on foot, walking tours are a great way to do that.
Their website is:
http://london.walks.com/
They have lots of interesting tours with outstanding guides.
As for what the touristy sites in London are, there are lots and lots of them. London itself is an attraction. It is an exceptionally beautiful city. Really lovely. It's without question one of my favorite cities in the world. I much prefer it to Paris (though I'm sure many would disagree).
If you're into museums, there are several wonderful museums in London. If you're not, you should at least make it to the Natural History Museum in London. It's the dinosaur museum that you may have heard of. Last time i was there entrance was free, so you don't feel badly if you just pop in and pop out again.
And nearby is Harrods, so it's not out of the way (nothing in london is really out of the way).
There are so many wonderful things to see in London, but you can get an idea by looking at that map i mentioned.
Then of course, since you're going for such a long time, you will have lots of time to explore beyond London. And again there is just so much to see. Hopefully some of the other people on the board will give you some ideas.
Personally I love Scotland, but I don't know if you want to go that far north.
I'm a big fan of Edinburgh. It's a beautiful city as well. And Scotland in general is quite lovely.
But I'm sure there will be wonderful suggestions from others on this board.
I just remembered theatre. You should plan on at least one evening at the theatre in London. My personal preference is for musicals, although i don't specifically know what will be playing when you're there.