So I've lived in this city for a few years now, and from the questions people ask me, it seems like there are a lot of assumptions made that should really be clarified. In all honesty, I've held a few of these myself, so this is no attempt to shame, just to educate.
#1: Alligators in the sewers
I'm not sure anyone truly believes this, but it's a big enough urban legend. No, you won't find any alligators in the sewers, just rats the size of alligators.
#2: Everywhere in the city is crowded
Manhattan is extremely crowded, and Times Square is pretty much abandoned to overpopulation. There are plenty of places in the city where you can stretch out, though. I live in Queens, and am actually able to reach out for six inches without hitting anyone. Plenty of space.
#3: Everything is expensive
The cost of living is high, indeed, but there are plenty of cheap things you can do. You can go to the zoo ($20), have a beer ($10-15), or a soda if you're not a drinker ($5), or just stand still and breathe the air ($2).
#4: Everyone is angry
You'll find plenty of angry people on their way to work, and I'm one of them to be sure. There are plenty of happy people all over the city, though. They're called tourists!
#5: The city is dirty
The city used to be much dirtier. Years ago people just threw their trash into the streets, but once public trash cans were set up, people began to aim for the cans and miss before leaving their trash in the street. The city is only going to get cleaner now that trash cans are being removed in order to stop littering. Eventually the city will just be reclassified as one giant trash can and technically there won't be any littering at all!
#6: There is a lot of crime
The more people, the more crime, that's just statistics. Bad apples can be anywhere, and when the city has a few million people in it, there's bound to be a few miscreants. However, as studies show, crime is going down everywhere, and you can really see it in NYC. Nowadays you only hear gunshots maybe twice a week.
#7: People only wear black
NYC is very fashionable, and black has been in fashion for a long time. All the fashion schools and runways around here mean people are going for the riskier styles, too. So you'll see more than just black, but also some greys and maybe even a navy blue!
#8: It's very noisy
Again, blame Manhattan for this. There's a lot of traffic, and rush hour is hell, but on off hours things quiet down a bit. You can even go to a park or library and you'll only have to slightly scream to be heard!
#9: There are no plants
NYC is very proud of its parks and foliage, and even has a program going on now to count all the trees in the city. We're hoping to reach double digits!
#10: The air is too polluted
Blame that rush hour again. It can seem bad when traffic is at a standstill, but NYC actually has some of the cleanest air around according to the Los Angeles city council.
Hopefully this clears some things up and gives you a more accurate image of where I live.