Love love love The Wallace Collection - my fave museum n London (very near Selfridges - is it Manchester Square ? (have Mummy brain at mo) - especially like having coffee & nibbly in their lovely cafe. Like the Eye too but as someone said pre-book on line - I think if you are going by train they do a 2 for 1 offer outside school holidays.
Boat trip down Thames, lunch at the Chop House - again often offers with Evening Standard etc.
London Eye is good if you have not done it, but pre book. Then there is a lot of interesting stuff to look at as you wander east on the South Bank. Graze the stalls at Borough Market if your day is Friday.
The restaurant (the actual restaurant, not the cafe) in Tate Britain has a fantastic wine list. It's only open at lunchtime.
My partner and I are spending a day in London next week for my birthday. Any idea of things to do/see? Not too pricey. I like art/cultural things, walking around, maybe a nice meal out, maybe something a little bit different....Ideas people please!