If you're at all interested in plants you MUST go to Kew Gardens, preferably by river boat from Westminster. There's a really cool catamaran service from Westminster to Greenwich, Greenwich is oozing with history and there's a nice little market to mooch around.

I took the kids to the science museum last year, found it disappointing, felt it needed a bit of investment. The V&A is now ace. The design museum's nice if you're into that kind of thing and is on the river just by several Conran restaurants, as well as it's own Blueprint Cafe:

http://www.danddlondon.com/londonrestaurants/explore

I like the London Underground museum, it's in Covent Garden so nice for a pretheatre visit or diversion from shopping. If you like the underground then I'd travel from Westminster to Canary Wharf on the Jubilee line to look at all the terrific new stations. You can get a boat from Canary Wharf to various other places.

Hamleys is too busy and crap nowadays, and most of London's main shopping streets are full of the same international retailers as every other capital city. There are still a few quirky independents in the triangle between Regent St and Oxford St, including:

http://www.reckless.co.uk/shop.aspx

If you're after cheap Indian food then the most authentic you're likely to find will be in Whitechapel:

http://tayyabs.co.uk/
http://www.lahore-kebabhouse.com/
http://www.mirchmasalarestaurant.co.uk/

Although the ones in Brick Lane are more famous. Speaking of which there's a lot of interesting stuff going in Brick Lane and Spitalfields nowadays.

Give us some pointers on your interests and I can add more.