This is some stuff about travelling and sight-seeing which I wrote in another thread:
Most of the museums and art galleries are free unless you want to go into a special exhibition.
I would recommend The Science, Natural History and Victoria and Albert Museums which are all within walking distance of each other and South Kensington underground station.
The Tate Modern is a really good art gallery if you like modern art and is near the Millenium Bridge.
Madame Tussauds will only take you about half a day so you might want to do something else after that. Queues can build up outside so you may want to go earlier in the day.
Buckingham Palace is near Green Park underground station. There are quite a few parks near by and you can walk to other landmarks from there e.g. Trafalgar Square, Picadillly Circus.
The London Eye is pretty good but only half an hour and queues may be long.
I haven't been to London Zoo in a while but I've heard they have a new Ape Kingdom. Also they have no elephants.
www.tfl.gov.uk is a good site for finding out about public transport. You can use the journey planner to help with routes and journey times etc. If you plan to use public transport a lot i.e. underground and buses or will be staying for a while it may be a good idea to purchase an oyster card (for £3) as with this bus journeys are £1 (instead of £2) and underground journeys are £1.50 (instead of £4). If you are going with kids, under 11s are free on the underground and under 16 are free on the buses.
I don't know anything about clubs or lounges because that's not my sort of thing.