@Tusha123,
It has been a while since I traveled to London but I used to travel their quite a bit.
I agree it depends on what your idea of a trip is - how to do it inexpensive can be a whole lot different than someone who wants to pain the town.
In general - get a tube pass - it is cheaper and easier to get around the system is pretty easy to learn and people are willing to help if you just ask.
They usually have some really good theater - and you can often get last minute tickets often pretty inexpensive.
My favorite tourist site right in London - Tower of London.
My favorite oddball thing to do - Speakers Corner - and if I remember correctly I think Sunday's are the best day (do a quick search to see).
Food - I would try Indian food - London has a big population of Indians so the Indian food is particularly good.
Music - there is also a great variety of music venues again so much depends on what your interests are.
That is just my first high level since I really do not know what you are interested in and if you plan on traveling at all outside of London.