One of the best things to do in London is visit the free museums. There are a number of them around the city, such as the British Museum, the Imperial War Museum, the Natural History Museum, the Science Museum, and the National Maritime Museum.
This time around in London, I especially enjoyed spending a day in the park just people-watching. It was amazing to see all the business people running at the park or playing soccer after work. It was also amazing to see the afternoon rush of everyone trying to get home.
Quick Tips:
The day pass for the Tube is a good deal if you're not into walking or you want to go to different parts of London in a short amount of time. However, be careful of what time the Tube closes, because you don't want to end up lost at night because you missed the train.
Most hostels and hotels will have a London Guide for that month that lists all the events, restaurants, and stores, as well as a party guide.
Renting a bicycle might not be a smart idea because of the traffic in London, unless you're just planning on riding through the parks, which would be a good idea on a sunny day.
Best Way To Get Around:
Though London is known for its Underground, I found myself walking everywhere. For some reason, I bought the day pass on the Tube, but I ended up walking at least 7 hours a day. Doing this, I found that I enjoyed walking a lot better than I would have enjoyed riding the Tube, mostly because it allowed me to see more of the city. London is not so big that you can't see it all on foot, but if you have to be somewhere by a certain time, walking might not be your best option. If you do walk and you get tired, you're in luck, because there are enough Underground stations spread out all over the city that if you keep walking, you'll end up at a station and you can take that back to where you're staying.