Used to live and work in NYC, but never rode there (was out of biking at the time).

Here's my $.02 -- there are lots of places to ride there with relative safety. Not every street is bumper/bumper traffic all the time. Once she learns her way around, and can get to Central Park, I would say it's definitely worth having a bike there.

As for theft - don't spend a ton of $, and don't have too pretty a bike. Heavy locks and chains.

Go for it - but start her slow, and find others to ride with to learn the streets.