Hi Berg, I was in London with my 7yr old doing the tourist thing 4 weeks ago. It really does depend on what you like as London has something for everyone.
I'll list some of the stuff we did below. It was all pretty awesome, but as said by others its a capital city and they can be expensive.
The British Museum (free)
- Excellent Egyptian collection including the Rosetta Stone and more mummies than you can shake a stick at.
London Museum (free)
- Covers London through the ages, Roman - Great Fire - Plague - even has big gallery with the actual London Olympic torch which is pretty cool.
Science Museum (free)
- Large Space exhibit with replica of appolo 13 moon lander, aviation gallery with full size planes. Many Interactive galleries.
- Natural history Museum (free) - didnt have time myself but its next door to science museum and people who have been there tell me its really good.
- Tower Of London (£25ish full price) - Essentially a large castle which houses the crown jewels. You can walk round the walls and most outer towers have their own mini exhibits. Central white keep houses all the suits of Armour which if you like medieval time period is very cool.
- HMS Belfast (£20ish) - WW2 Destroyer on the Thames near Tower of London. The ship has been turned into a museum and gives a great insight into those times. Lot of stuff on its part in the engagement with the Sharnhorst Pocket Battleship. Would recommend highly only if your into that kind of thing.
- London Eye (£25ish but can get deals to link it to London Seaflife centre, river cruises, shrek 4D ride etc which are all owned by same group) -
I liked it, felt expensive for what it was but its an iconic landmark and we wanted to go on it. I dont regret it, Houses of Parliament is just down the road too.
Also go on in the dark, I didnt but wish i had.
I would also highly recommend a river cruise, or a speedboat version. Top of my list for next time.
- London Zoo (£20ish) If you like zoo's its a good one. Its at the top of regents park which is really nice walk and has a nice chinese/tai restaurant on a floating ship nearby.
Theater wise cant help too much, we went to see Charlie and the Chocolate Factory which was amazing, as was the walk back to the tube station at 10pm when London was lit up.
Two bits of advice would be ....
1. Use the tube, it really is the optimal way to get around and pack as much in as you can. You can get a weekly ticket which has unlimited travel allowed. This means no buying tickets everyday which is a mission in itself. Check if its cost effective, was for me as kids travel free on it.
2. Plan your days. Cannot stress this enough. Know where you want to go and how to get there. Which underground line and destination of the train you need are very important, it is very easy to end up on wrong platform and train.
Other than that have a great time.