What to do in New York (traveling alone)?

Ok so in 2014 I want to create fun memories! I'm be going on my own as I have no friends haha and I don't know anyone in New York so. I'm 18 and planning to go for 7-10 days in April, I've never been on an airplane! I already have planned going to imats (event for makeup lovers :D) and I'm going to see the statue of liberty, of course. Any other cool things I should know of? Shopping stores you like (I'm not rich!) haha but I got money to spend apart from other traveling costs. Ummm oh yeah, advice on finding a hotel? And how much do you think they would charge for 7-10 day stay? I know it's gonna be expensive. I also hear about times square a lot, what's there?