London Travel Tips

Make sure you use the oyster card or visit oyster card, there is a deposit of 5 pounds, but you can refund that later on. The good thing is that it caps daily, ~~weekly~~, and monthly . Apparently, oyster card does not cap weekly - you have to explicitly purchase a 7 day travel card for the oyster. One day is around 8 pounds and 7 days is around 32 pounds plus 5 pounds deposit for the card, which you can refund later.
Otherwise, top it up for 7 days or monthly.
You can buy it in convenience stores/shops and the tube stations.
You can get a visitor oyster card, see here for details

This really depends but you can get an annual gold card to get discount on train tickets, otherwise, you can also get the weekly or monthly pass.

Try to get the following annual membership, it will still turn out a lot cheaper

This really depends.. it can cost from 150 - 200 pounds depending if you get standard or premium pass
You can probably save if you really go to Legoland, London Dungeon, London Eye, Madamme Tussaud's, Sea Life, etc.

If you like visiting ruins, castles, e.g. Dover Castle, this is really worth it
For 39 pounds a year, you can visit over 100 of sites around the UK (and can even get discount in Edinburgh's Castle)

It costs around 40 pounds individually (cheaper for a family)
It will save you a lot since if you go to at least 2 places, you can most likely break even already

Tower of London - around 20 pounds
Hampton Court Palace - around 20 pounds
Banqueting House - around 8 pounds
Kensington Palace - around 16.50 pounds
Kew Palace (unfortunately, you have to pay to get in to Kew Gardens to reach the Palace) - around 10 pounds

This is for most visitors and worth if you are visiting at least 4-5 attractions. Do not take the with TRAVEL - I suggest take without travel and buy the oyster card separately.

Just ME...