Pretty much just restating whats already been put out there. Yes it'd be nice to get a place in Manhattan, but like everyone else has said, it's going to cost you an arm and leg. I live about an hour away from Manhattan by the LIRR, and anything around where I live is considerably cheaper. You can always just take a train into Penn Station which will bring you right to the center (sort of) of Manhattan.
What are you going for exactly? First trip to America, should probably throw out what you're trying to accomplish/see. Manhatten has a ton to do, but theres also a lot of things to do/see in the areas around Manhattan as well. (Not that you could really run out of things to do in NYC for a 2 weeks...)
Walk/Subway everywhere. I've only had one bad experience with a cab once, but I'll just put it out there. I was obviously looking like a tourist since I had a ton of bags/backpack etc, got a cab and asked to go somewhere. Some streets are one way (maybe all actually?) and he was skipping turns to get to our destination faster just to get more money. May be different for you, but just saying, you never know. Walking is generally the way to go.
If you're around Central Park, I know I've seen some guys who rent bikes out to ride around the park. Not sure of the price, but they are there. Restating the above, I'm actually surprised I haven't seen a cab hit people on a bike. I'd rather skydive with a faulty parachute then ride a bike on the streets in Manhattan.
Summary:
-Being a train/ferry ride away from Manhattan will save you money.
-Walking/Subway is the way to travel. (It can get VERY hot, plan your day trips accordingly)
-I thought I'd have more bullets of information, I guess I was wrong.
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