The Tube (London Underground) is incredibly easy to travel around London. As you've got an iPad, take a look in the App store and get hold of one of the free Tube Maps - there's loads of them. This will help you plan out which stations and lines you'll need for your day trips.
On my last trip to London about 3 years ago, I was surprised at how much more pedestrian friendly it was too. Take good walking shoes and hoof around - the people watching and interesting nooks and crannies are best seen from the street. about 5 years ago
The Tube is really great, but can still be expensive if you are buying paper tickets or one way journeys.
For maximum savings buy an Oyster card from most Tube station selling agents for under £4 and load it up with cash. It'll automatically cap your payments at the price of the day pass calculating the times and zones where you've used it or, for even bigger savings, you can preload it with a weekly or monthly pass for unlimited travel in the zones you'll use it most. If you then use it in a different zone it'll only charge you that journey's price difference.
Hope this helps! about 5 years ago