I know it's a bit late to reply, but I work in central London (just down from Parliament Square).
I'd second most of what Tobian said - the museums are well worth a visit (I love the BM and the London Museum at the Barbican) as most are free. I'm also fond of the Imperial War Museum (on the South Bank), the RAF museum (north London) and the National Army Museum (Chelsea). I can't comment on the pubs - I have yet to find a good one that's decently priced
Unfortunately, Page's, the local Trekkie pub (complete with a 6 ft Enterprise hanging from the ceiling), is long gone - it's now a wine bar. I found this a little depressing, it's where I met my wife.
The only games shops I know are in central London (Playin Games - on Museum street just around the corner from the aforementioned British Museum, and Orc's Nest at Cambridge Circus on Shaftesbury Avenue) or the north (Leisure Games is in Finchley). Forbidden Planet stocks a small selection but they're overpriced, although the place is also worth visiting for the display of genre figures and models in the windows.
Jon
"There are worlds out there where the sky is burning, where the sea is asleep and the rivers dream; people made of smoke and cities made of song.
Somewhere there's danger, somewhere there's injustice, and somewhere else the tea is getting cold. Come on, Ace, we've got work to do."
THE DOCTOR, "Survival" (Doctor Who)