I went to London for the first time a few months ago. I recommend leaving the laptop at home unless you absolutely need it. First off, hauling a laptop around is a hassle. Second, open access points were few and far between. I stayed in three different hotels and not one offered free wifi, they all charged about 10-15 pounds for a day's access.
If you're there to sightsee definitely check out the Museum of Natural History, it's free and it's in an amazing building. Additionally I think the hidden geek treasure is the Grant Museum of Zoology. It's small but worth stopping in too if you like preserved stuff in jars :)
Also, Oyster card! Get one. I actually found that taking the double decker buses was a nice way to get around and see some of the city at the same time vs. the tube.