Let me start off by talking about travel. Driving in London, is not fun. So I suggest you buy a day travel ticket and use the tube and bus to get around.

All the public museums are free so that’s a great place to start.

British Museum – www.britishmuseum.org : This is the biggest one. It’s near Tottenham Court Station and their collection is huge.

Natural History Museum - www.nhm.ac.uk : Has some nice dinosaurs. Near High Street Kensington station.

Imperial war museum - www.iwm.org.uk I enjoyed this one the most. They have the turret, from a Second World War battle ship, outside. It fired shells the size of mini’s, I kid you not. Inside they have a V2 rocket with the side cut open and hanging from the ceiling they have various World War 2 planes. It’s near Waterloo station.

Between Monument and London Bridge stations runs the Thames river and there is quite a bit to see there. At monument station there is an interesting looking, well monument. Between the 2 stations you have London Bridge which is worth a look. In the river you have the HMS Belfast ,that is a Second World War vessel, that took part in the Normandy landings. Going onboard is £10.30 and free for kids, but nice to look at from the outside also.
In the same area you have the tower of London. Worth looking at from the outside going in isn’t cheap but they have the crown jewels in there if you want to see them.
Map of the area:

Bucking Ham Palace – Worth a look. Jump out at Victoria station. You can see the soldiers with those large funny hats. In the area you also have St James and Hyde Parks ,which are real nice, on a summer day.

Trafalgar Square – Several things to see here, most famous is the Nelson’s column which was built to commemorate the victory of Admiral Nelson over the French fleet at the Battle of Trafalgar. Near Charing Cross station.

Big Ben – Large clock tower and part of the Houses of Parliament. It can be seen best from the London Eye. Near Westminster station.

Soho – If you look at Oxford Circus, Piccadilly Circus and Tottenham Court road stations. It forms a triangle on the map. Inside there is Soho, it is a 200 year old adult shop area. Call me a pervert but I enjoyed going, not for the kiddies though. Towards the Piccadilly and Oxford Circus areas you have the heart of London’s shopping district.

Tate Modern – This is an art gallery, most of the exhibits are free, some are not.
It’s near London Bridge station.

Borough Market – It’s a food market. Get your eel pie here. Open Fri noon-6pm and Sat 9am-4pm and near London bridge station.

There’s that and much more to see in London.