I agree with what Lee said. How many days will you be in London? Will you take day trips on any of these days?
For help figuring out how to navigate London, read a few guidebooks and study the Transport for London website (www.tfl.gov.uk). Once you're in London, look at this website every morning for Tube closures and "planned engineering." They worked on at least one Tube line every day that I was there, and on the weekend it wasn't uncommon for one entire line to be closed. Buses will help you avoid the problem, though generally they are slower than the Tube because of traffic and frequent stops.
When you look at hotels, I'd suggest picking one that has good access to a couple of different Tube lines in case one is closed. I stayed at Vancouver Studios in Bayswater; that hotel is just a few minutes' walk from the Queensway stop on the Central line and the Bayswater stop on the District/Circle lines.
The Tube took me a couple days to learn. You have to pay attention to which direction you're going (northbound, southbound, etc.) because the system doesn't provide endpoints the way the Paris Metro or Chicago El do.
My strategy for visiting the Eye was to wait in line to buy tickets. The line was long but moved quickly (this was on a Saturday evening in September with great weather). After you buy tickets, then you have to wait in another line to get on the wheel.
For the Tower of London, my friend and I "lucked out," if you can call it that. This was the next day, Sunday, and it rained and was chilly. We just walked up and bought tickets. There was no line and the site wasn't even very crowded.
If you like museums, plan to spend a lot of time at the British Museum. I picked a few areas of interest (ancient Near Eastern art, Egyptian art, the Rosetta stone) and explored those in depth, rather than run around the whole place trying to see "everything."
Westminster Abbey and St.Paul's - check out their hours of operation, pick a good time for you, and stop in. I recommend the audio tour for both places - they're well done. In St. Paul's I climbed all the way up to the top of the dome; the views are fantastic.