There was some worry over the last year, but things have quieted down in the last few months. The big changes are mostly localized to the high end of incomes, where lifestyles have been downsized a bit. Non-profits that depend on wealthy donors are putting off plans to expand, and it may be easier to get seats at a popular show or a table in the most exclusive restaurants.
The streets are not filled with bankers who were making hundreds of thousands last year and are homeless this year. The subways are still crowded and no more or less clean than last year.
It's a big city, and it's not going to turn into a warzone because Lehman Brothers closed.
I live in SF, which is not cheap at all (second most expensive market in the US), and I think NYC is ridicusly overpriced. A software engineer in NYC makes less than in SF, yet the cost of living are at least 30% more (rent and groceries, and everything else). and you have to pay a NYC tax also.
No wonder there are no startups in NYC.
The only great sides of NYC, are it's nightlife, and lots of girls (meaning even if you are a dork, you will get laid). When it comes to dating, SF/Silicon valley, is a dessert in comparison.
In terms of jobs, I knew of a few people who've lost theirs but they were able to find new jobs in a matter of a few months.
So again, I don't notice much slowdown in NYC. In fact places in brooklyn such as Williamsburg, Carroll gardens, park slope are growing in popularity and people are moving to these for slightly cheaper rent than in the city. A few years ago, I remember that these places used to be very crappy and run down. Now they are blossoming.