Help - visting New York?

I'm planning on visiting New York at the end of September for 4 days, I'm just wondering where would be the best area to stay in order to be right in the middle of the tourist attractions and central park. Also can you recommend a cheap, single traveller, friendly place to stay? Also if anyone knows when the best time to book flights would be and where is the cheapest place to book for American flights that would be awesome - Thank you in advance :)