I have only had a quick flick through the thread so apologies if these have been answered.
If you are going to Abbey Road they have a little sign where you can go on a website can get a video clip of you walking over the the road. It's free, I havent done it so don't know the quality but free hey!
Also citymapper is an awesome app, I also would recommend bus london and tube map.
Someone also talked about going to the theater - getting good seats is expensive and often the ones on sale at the booths in and around Leicester square are not that good so check the seat map first but you can get some bargains. I would take a look at the national theater on southbank as well they have some really interesting performances/shows there and are often cheaper but more plays I suppose than musicals. If you can see something at the royal albert hall that is a great place - we saw cirque de soliel there this year and it was pretty good. I have not been but if you like opera a lot of people rave about the royal opera house too.