What neighborhood should I live in? (Brooklyn and Queens)?

In Queens... Astoria is a very safe place to live, I go to school every day over there. The N and Q trains usually come every 5-10 minutes on weekdays and you can easily transfer to the 7 train to Manhattan at Queensboro Plaza. Sunnyside and Woodside are also very very safe and quiet neighborhoods to live in. I lived in both neighborhoods almost all of my life and there are a variety of buses that go to various locations. The 7 train is also right on Queens Blvd. The apartments are also decently cheap within your budget, I suggest you look on Craigslist for some apartments first tho. Good luck.