Well I just got back from NYC and I have to say...prepare to have a great time!
You're going to NYC so you are going to spend money. There is no way around it. You could try the Doubletree in Times Square because you will be right in the middle of the action and it won't kill your bank account. However you are staying for two weeks and two weeks in any hotel is going to cost money.
If you are staying for 2 weeks I'd suggest getting a NYC travel book from a bookstore. The money upfront will save you BIG money when you get there. You can spend lots of money in restaurants so these vacation books shows you the places to get good food for moderate prices. NYC is expensive and can get REAL expensive after two weeks.
If you are looking to shop and get cheap "knock-off" jewelry or bags...go to Chinatown...and use the black market. I'm not kidding! Just walk through Chinatown and you will see folks on the sidewalks. It is common. Cash only of course.
Little Italy is great for food and the restaurants cut deals right there on the sidewalk in front of their menus.
"Freea drinksa for a the kidza...We gotta the pizza and the parmigiana."
Don't walk in the first place you see, look at all the menus in Little Italy.
Statue of Liberty is great but go early in the morning as the lines get long. The Empire State building...do that at night as the lines will be MUCH shorter.
Also, speak to the Grayline Tour Bus guys. They are on just about every corner and you can get great deals for all NYC attractions and shows. They are the tour buses and they do an uptown loop (from Central Park, WTC Ground Zero (which is now a construction site) the waterfront, etc.) They also do a downtown loop that goes through the other side of Manhattan. They also do a non-stop night loop through Brooklyn which is great. During the day these tour busses stop frequently so you can get off and get back on. They are constantly running and wait time for us was minimal. Some buses are right behind each other. These tour busses have the open top and that was great. Each bus has a guide and points out areas of interest.
Avoid the Brooklyn Diner near Times Square. It is a great place but I had a tough time spending $16 for two eggs. The word "diner" was deceiving to me. If you sit down at a place and your eyes pop out of your head when you see the prices do not be afraid of getting up and walking out. It's your money and they will forget about you as soon as you walk out the door. I wish I did that at the Brooklyn Diner!
Any other questions?