Best(s):
Area around Covent Garden, there's all that live theatre in those parts.
V&A Museum - just so much fun and things to see in one place... And the Science Museum, next door is good, too!
Camden Market - it was better before they "improved" it... but it's still okay.
Portabello Market - not necessarily inexpensive, but an interesting selection.

Worst:
Tate Modern - I pity any art work there... the humidity must be murder on the works of art.
Clink Museum - Disney makes better horror... the rubber rats were a bit silly.
The Theatre Museum - it's supposedly in the V&A, but it was a lot better when it was a separate location.

Best:
I love the V&A (the Japanese room with the netsukes are a fave) and also the Tate Britain and I do like the Tate Modern, particularly its members café with views of St Paul's and the Thames. Living in London, and the galleries being free (except for special exhibitions) means that it's very easy to dip in and out and explore them each a bit at a time without becoming overwhelmed.

I'm also a fan of Hampstead Heath and I always take visitors to the top of Primrose Hill, particularly on a warm summer's day, where you get a good view across London accompanied by a glass of sparkling wine.

Worst:
While there are dodgy areas all over London, I generally feel quite safe. It's just a shame there are a lot of ugly buildings, around Old Street, for instance. I do get annoyed by guys trying to sell me weed on the Camden High Street when I'm on my way home.

I also don't like finding the Jubilee Line (or most of the tube network) is shut down over the weekend for upgrades, particularly if I need to get somewhere — not to mention the price.