Can't wait to return!!
Great city to visit, so much to do, if you want to do a lot and only have a few days I suggest picking one museum to visit during the day(max 2) and really take it in, then maybe a show at night, there is a site if you google London theatre that will give you discounts on tickets for that day/following few days, also try last minute.com for cheap tickets to a show. Book Harry potter, the Lion king and miss Saigon in advance because they sell out weeks in advance
Insider Tip:Buy an Oyster card for intercity travelling, they save you so much money, one night my bf had to pay £9.40 for a one way into Central London, while only £2.70 was deducted from my Oyster card. You pay €18 for it initially and you get €15 credit on it, you will use all of this and need a top up, but whatever you don't use you can refund