For those of you reading this for actual advice, instead of my random ramblings on topics you prob don't care about ;), here are some tips!
APARTMENTS
Options -- you can hire a broker and pay them a large fee. This is easiest, but the most expensive. Get a 6 month or 1 year lease, etc. Or, you can get a lease without a broker fee (look on craigslist for the "no fee" ones).
If you want something more temporary, you can sublet (sometimes legal, sometimes not). Go on craigslist and look for "sublets." Some are long-term. You can also find roommates on craigslist. This is a less "stable" option, but usually you can give 1-months notice and move out. Where as with a lease, you're usually stuck for the full time.
Most will ask that you give the first month's rent with a security deposit and sometimes a last month's rent also (so if your rent was $1500, that'd be $3000-$4500 up front. So yeah, bring some $ with you. SCAMS -- there are a fair number of sublet scams where the person gives you (and maybe 10 other people) a key, after taking your money. This is a risk you take from not doing it the "regular" leased way.
Always ask if there has been a bug/rodent problem (they might not be honest, but sometimes will). Other questions you may care about:
*Is the hot water in the shower nice and warm? Or freezing/steaming hot alternately? Most newer buildings won't have a problem with this.
*Is laundry in the building? (easy and nice, especially if you have an elevator). Or is it down the block? Or several blocks away? Yes, you will be that old-lady looking person pushing a cart. A lot of people do it, but it's still an annoyance. You can also pay to have your laundry picked up and delivered, but it's expensive of course.
*Where is the closest grocery store? Nightlife?
*How far away is the subway (this is huge, unless you enjoy killing 10-15 minutes walking to the train). Also, ladies if you're wearing heels to go out, and plan on taking the subway being farther away is obviously an issue and you may have to take cabs more often.
*Is the apmt. street level and facing the street? You may have a serious street noise issue.
*Does the cable/phone actually work? Is it provided in the rent fee?
*Does it have an oven/stove? Or just a microwave? Many apmts. do not have dishwashers, and you'll need to wash them in the sink.
*If there are roommates, are they considerate? Clean? Quiet? On drugs? Will they ask for/steal your money or things?
*Is it a "walk-up" (meaning stairs only). Or does it have an elevator. Walk-ups are common in the East Village, West Village, and the Lower East Side.
*Most people go out in the neighborhoods mentioned above. If you're going to live way uptown, or in Queens, NJ or Brooklyn, keep in mind you'll be getting cabs after midnight or so back home (if you're a girl concerned about safety -- if you're a guy or don't care, then you can take the subway back). A cab to the Upper East Side from the Lower East Side could cost you $15-$20 depending on traffic and how far you're going.
*New buildings often have amenities like gyms, laundry in the building and other services. Older ones often don't, but may be in more popular areas. New buildings in popular areas are hugely expensive.
MEETING PEOPLE
It's hard to meet people in NYC. However, it's a huge city of 20-30 somethings (many of whom are single/looking for friend). People are also super busy. Most people don't really strike up conversations at the grocery store/or on the subway, etc., though some do. Your best bet may be to join meetup.com, join a sports league (zog sports is good), do a brunch group or something like that. You can also take some sort of classes. Or many people go back to school part-time, MBA, etc., as those are very social programs and you'll meet a ton of people. You can also get into various kinds of dancing (salsa, or that bollywood style is becoming popular) or other things like that.
DATING
NYC is a city where the majority of singles are on match.com, but don't tell others. Almost all of my single friends have been on there at some point. They've told me, but not most others. There is no shame in doing this, and it's a very easy way to meet new people also (sometimes even friend). However, watch out for players! Guy players and girl gold diggers. There are nice people mixed in as well, but don't expect to meet your match in a month. It may take you 50 dates, or even 100 dates to meet the right one, so you'll need to hang in there -- or you could get lucky and find someone fast too of course! But keep your expectations realistic. You can also meet people in bars, though a lot of players/golddigger congregate there. Still, I know a few people who've met quality people at bars. Through friends is a great way also, but you first need to make friends (see above).
GROCERY STORES
You can get delivery from fresh direct. Or like most people, walk a few blocks to the grocery store. Carry a little red basket. Buy about 2 or 3 bags worth (as much as you can carry home). Or get a cart, but that's kind of unusual. Most people buy small things like some yogurts or milk , etc. Make many trips to the store and you won't have to carry as much. Combine this with your delivery meals (which will probably cost as much as the grocery store anyway), and you're good to go. It's easy to get fat here of course, so you may have to pay more attention to this. Buy a bag of salad, some plain non-fat yogurt, some plain oatmeal or cereal, whole grain bread and some fruits and veggies, and keep that healthy boring food around, so you don't completely pig out on pad thai and chinese every night. You can order in healthy also, just be careful and maybe eat half a big meal and take the rest for lunch the next day.
DELIS
These are those little stores that seem to be on every block. Also called Bodegas. They are surrounded in plastic, usually with flowers and sometimes produce on the outside. The door may seem invisible to you at first, but it's there -- it has a little metal handle. If you buy flowers, you usually pay the litle guy sitting outside of the deli. Sometimes same goes for produce. There is usually a sign though. Delis are tiny, and may or may not actualy have deli items (like potato salad and meats to be sliced into sandwhiches you can ask for at the counter). Some have only drinks, some dry foods, cans of soup, some candy, etc. Make sure to have your money ready at the counter as the cashiers are not friendly and the people in line are in a rush.
BARS
You will end up drinking more than you expect here. That is, if you live in the city (or close to it) and don't own a car. It's easy to drink and most people go to happy hour occasionally and mimosas or bloody mary's are staples at brunch. Your tolerance may go up. You can definitely get by drinking less, but just be aware that NYC is basically one giant bar. Lots of nightlife here.
PETS
Apartments are tiny. So dogs here are tiny also. Cats are popular. You may have to get a dog walker if you have a busy job and aren't home a lot. You may have less time than you realize, so wait and see what life is like before bringing Fido. Big dogs are pretty usual unless you have an enormous place and dog walker, though some people cram them into small apartments. This bothers others who feel dogs shouldn't be cooped up. If you live by a park, there may be a dog area.
FASHION
People are into fashion here. Even if you don't care at all, you'll likely pick up some style while living here -- guys also! It's unusual for someone to look completely horrible here. However, there is everything here. The bum look to the Upper East Side little pearls and cardigans and guys with boat shoes and litte sweaters, to the grungy Lower East Side punk/hipster/vitage thing, to the Williamsburg hipsters, and the West Village "rich casual" thing. You can get away with whatever, but people here do value fashion. That doesn't mean you need to spend a lot of money though. Make note of the basic "in" styles and get knock offs that look nice and you'll be just fine. Guys, don't wear ugly shoes. Girls here really notice guy's shoes.
SIDEWALKS
Don't stand in the middle of them. Be aware of the space you are taking up and who is trying to pass you. Pass on the left if possible. Stay to the right if you are very slow. Don't weave around when walking -- stay in a straight line so you're easy to pass if you are slow. If you have to text or look up directions on your phone, stand to the side next to the buildings so you're easy to pass. Don't just stop in the center of the street -- this is one of the most annoying things about tourists for people who live here. Try to walk no more than 2 next to each other when with a big group.
SHOES
If you're walking far, let's say 5-10 blocks, you can either take a cab and wear heels, or bring heels in a slightly larger handbag (put them in a plastic bag if your shoes might get dirt in your nice bag), and change your shoes as you get to the bar/club. They sell little ballet flat things also that fold up and you can put them in your bag. Not everyone does this, but some ladies also kill their feet walking in heels and end up needing physical therapy or even surgery -- ick. For my shoes, I have 5 block shoes, 1 block shoes, etc., meaning the distance I can walk in them without being in pain. I keep this in mind depending on how far I'm walking when I leave to go out.
You'll need to get waterproof shoes for slushy show. Snowboots that are waterproof, or rainboots are fine (a lot of people wear rainboots on slushy days). Otherwise your shoes/pant legs will get all wet, and maybe ruined if you have leather shoes.
COATS
You'll have to get a good winter coat. Wool, down, etc. The long black wool coat is very popular on guys and girls. Also good is gray. Or shorter coats for less cold days. You'll want to wear some layers under, let's say a shirt and sweater. Black tights are very popular on girls, with heels, boots or ballet flats. Big puffy coats are fine for day but are less popular for going out. Coat checks are at restaurants and bars. You give them your coat, get a ticket, pay $1-$3, and may tip. Sometimes they charge you more if you have a coat and a bag (shopping bag, purse, etc.) Keep your ticket and give it to them when you're ready to leave.
EXERCISE
People go to gyms here, but not as much as other parts of the country that are warmer (because we can hide flab under coats). A lot of people run around the city, or jog in central park, or play sports like soccer or basketball in parks. Yoga is big.
If you have questions about other topics post a comment and ask me! Hope these ramblings were helpful :)