If you just want to explore at your own pace and see what you can see, then undoubtedly walking will be your best option. You may even want to rent a bike — now, that does not mean going on a bike tour, although that is available as well. However, renting a bike just for you — and whomever you are with, of course — will allow you to set your own pace.
For sightseeing, the double decker buses are a whole lot of fun, and you will get to see all of the most famous sites.
And if you are just hanging out, do not be afraid of the Metro.