I'd add a little bit on to a lot of this too, if you're a tourist you'll generally be in areas where it is a touch cheaper.
Oyster is really a no brainer, it can cost you double if you don't have one.
The Eye is only £15, St Pauls is £10, really depends on what you want to see. You see more on The Eye, but inside St Pauls is awesome.
I actually recommend the open top buses to people, they great, and make sure you get the boat trip too. The commentary is brilliant and yuou won't get that by walking round or getting the tube.
If you need to save a bit but still want to see some great stuff, do 2 things, invest in a good guide book and walk around central London, you'd be amazed how many things you walk past you don't even notice. Also go to many of the galleries and museums that are free (Tate, Imperial War etc)
Club entry can vary from a fiver way up depending on where you go.
As I've said to a lot of people, it's not cheap, you might need £60 a day maybe more maybe less, but if you're coming and want to see it, don't try to be the mega saver. There are ways to cut costs and stuff to do that is free or cheap, but you have to spend to enjoy London, it's just the way it is