There is soooooo much in London, i dont know if i would travel outside unless there was something special.
Everytime ive been to London, ive never got on the Hop-on-Hop-off bus. If i remember correctly, Rick Steves mentions in his London book which local buses do just about the same as the Hop On bus. ALso, i think they are on the spendy side like 20 USD or more per leg.
I just love the tube system there. I have a Oyster card that i bring with me everytime i go back. Its easy to use. But i prefer to use the tube system there. If you want to be adventurous, just pick a stop and head on out. its sort of like prairie-dogging on a large scale instead of cubicle land.
If you care to:
look at going down to the Westminster/Parliament area. Its iconic, but i like the area and its soooo London.
Just walking around London is cool. You never know whats around the corner or the view you will get.
the British Museum is really great too. If you have the time, you may want to peek inside. But that would depend if you like Museums. Trafalgar square is nice especially if the weather cooperates.
I havent been in Hyde park other than on Horseback. one day i will make it on foot.
there are alot of museums in London too, but i would probably spend more time outside than in, unless the weathers bad.
If you can, spend some time grazing on the local food and stuff. I like going on a dessert hunt to try to find different and yummy treats. I did find local candy store that has some great caramels (toffees).