If it's still running in January
go see The 39 Steps at the Criterion, Piccadilly. It's terrific fun, and jolly amusing too. Go have a look in Fortnum and Mason while you're there too.
A tenner will get you a ride on a rickshaw (useless for actually going anywhere, but it's a fun ride)
Speaker's Corner on a Sunday morning for arguing fun.
(rnuk http://flickr.com/rnuk, Thu 13 Nov 2008, 10:31, archived)

excellent
she loves the 39 steps.

EDIT: gah, we're there sat till mon evening, and busy the sat night. There isn't a sunday show or a monday matinee. good shout though, thanks.
( RR I love you ... in a way, Thu 13 Nov 2008, 10:33, archived)