What parts of the city would you avoid if you were a tourist in town? Obviously you need to be careful in Harlem but what other areas would you consider dangerous. (to walk by day)

In my area (Brooklyn) I'd say Bedford and I always avoid most of the Bronx these days.

Ive had some scary moments in the Lower East side, usually at night. It all comes down to how well you look like you fit in. You can get mugged around Washington Square if you have a nice watch on!

I have only had a run in once about 2 years ago on the subway near Greenwich Village. Almost got mugged, but scarred the asshole off.

most people don't realise this but NY has quite low crime

here's a good wikipedia entry on crime in new york:

http://en.wikipedia.org/wiki/Crime_in_New_York_City

Harlem. I was bashed walking to friends place a few years back. Not a very nice experience.