You will find most things here pleasantly inexpensive, as most people are saying here.
I have a friend who lived here who was from Manhattan. He recently returned to NYC after two years and he always told me about how expensive it was there and how cheap he lived here.
You can do the same.
Temporary apartments are a tad expensive in comparison to long term leases. But you can EASILY find a nice temporary apartment for far less than $2200 a month that should suit your needs. Temporary apartments are all furnished. Longest lease you can legally do on a temporary apartment is 6 months, but you may be able to make a deal with someone for more time, or just renew at the end of 6 months if they let you.
If you can get to the point, once you've moved here, to find a way to rent an apartment on a long term lease, you'll save yourself money on the lease (1/3 to 1/2 the cost of a temporary apartment for the same property, roughly, depending) but of course then you have to think about furnishing it.
Refrigerators, washers, dryers, etc, are a bit on the expensive side. Furniture can be a little expensive.
I'm basing costs on comparison to Houston, Tx, which is one of the cheapest big cities in the US to live in. I can just live here, NICELY, for a little less than I would live there in about the same style.
You being from Manhattan, I don't think you'll have much problem with these kinds of things price-wise.
Computers, cellphones, cameras, etc - like the others said, stock up on everything you will want that you can carry and bring it with you. That is one of the things that will cost you far more than what you can buy them for in Manhattan, or anywhere in the US for that matter.
You will find that things are not engineered as well here, for the most part. Things are not finished as well. You will hear things like incessant pounding on the walls with a hammer because all buildings are built of bricks and the plumbing and electrical cabling are run through them. When someone is remodeling or repairing pipes or cables, etc, they have to break the walls open and find the item they want to work on. That's the hammering. It's a pretty common occurrence in the city in apartments. After awhile you don't notice it so much.
It will take some adjustment. Living as an ex-pat here is not for everyone, but if you're tolerant and willing to make some sacrifices, again, like the others have said, living here can be very nice overall.