I have heard nice things about the Royal Ballet/
Doesn't surprise me. The Royal Ballet is an internationally renowned classical ballet company in England.
I would love to visit London and see it,
Tourism is a key industry of London. If you wanted to go you should contact London & Partners for travel info.
What information would they provide?
Information for touring London. They are the evolution of the old London tourism company.
What else is there to do in London?
You could always visit one of the commonly known tourist attractions, such as Big Ben, which I heard was recently retired as a clock but still visible.
So the clock does not work anymore or what does retired mean?
It no longer chimes for the next few years because there is conservation work being done on it.