Beatles walking tour, do it. A guide walks you around all the famous spots with great detail and stories being told at the same time. Very educational and makes for some great pics.
If you get the chance, and you like gypsy jazz, try this place
http://quecumbar.co.uk/ . Great little venue and they always have super talented bands playing there.
In general, if its your first time, do the bus tour. Sit on the top, in the front, avoid human guides, plug in your headphones and listen to the audio guide like that and literally go around that entire map like three times. You get to see allot of london that way. And repeating the circuit multiple times will make sure you don't miss things and that helps for things to sink in.
Also, once you have figured how to use the public transport and you know how to get home from where ever you are, get lost!!!!!! thats the best way to explore!!!