I was in the exact same boat as you in 2006. I'm from LA and I chose NYU and have NO regrets. You are right that you will never have a chance to experience NYC the same way again. While it's always possible to just move there when you want later in life, now is the time. NYC will change you're life! I lived there for three years and came back here(Los Angeles)after my MA at NYU.I'm so glad I experienced both worlds. I never really liked NYC that much but it toughened me up. Now I've got connections on 2 coasts.
There will always be time to make connections at USC and UCLA without being a student. There are so many ways to make connections without being in school in LA since SOCAL is a mecca swarming with filmsters. Go to NYC for a little while and then come back. Both will always be around and no matter what you're age or what anyone says, you'll always have time to make connections in LA. Don't rush it. Don't be sooooo focused. Try new things. It will help you tog et a change of scenery. Don't leave a chance like this in the dust. Live life a little and grow strong as a filmmaker and theorist by branching out a little. Trust me on this.
Telling other LA film junkies I was in NYC makes them jealous, want to talk to me and gives me a colorful history, is an icebreaker and has just enhanced my life soooo much.
Go to NYC and then come back to awesome LA when you are done. You won't regret it.