You said your parents love museums. In London, go to The British Museum, and The Victoria And Albert Museum. These museums have a great variety of exhibits, so there will be something of interest for everyone. Spend two complete days at the British Museum. (One if you are short on time.) Spend one day, or at least half a day, at the Victoria And Albert. Both museums have cafes, so you can have lunch there, and then continue seeing the exhibits.
You may enjoy the Tower Of London. Used in ancient times as a royal palace and a prison.
You may enjoy Westminster Abbey if you or your parents are interested in cathedrals.
You said you and your sister will be looking for something fun to do. You may like The London Eye, which gives you a birds-eye view of London. You may enjoy a boat ride on the river. The entire family may enjoy a ride on the Tour Bus that goes by all the most famous tourist sights in London. There is a host, or narrator, telling you what the sight is that you are passing by, and its history.
A good way to get a quick view around London is to take one of the Hop-On-Hop-Off bus tours. One of the companies that does it best is the Original Tour. They go by all the "must see" sights of London. And you can hop off anytime you want, look around a sight, then get back on the next hop-on bus that comes by. The tickets are good for 24 hours.
I would use the hop-on-hop-off bus as a way to give you a tour around the city, but regular red double-decker buses are the way to go for just traveling around London every day. In addition to the tube, that is.
That's just a start....there's so much to see in London! Hope this helps!