Where do I start if I want to leave my current life, move to NYC, and start fresh?

Creative opinion second, pragmatism first:
Save money.

You need ~2 months' living expenses prior to moving. And 2 months doesn't mean rent x2 + food + hooker cash.

Consider that you'll also need a security deposit, some furnishings, metro cards, and maybe even a license pending the strictness of employers' paperwork.

Oh, and that even when you're "hired" it could take 1-2 more weeks to set up payroll and get your first check.

So, there's that. I'd say minimum $4,500 ($1,500 rent/utilities x2, $400 /month groceries, $350 /month miscellaneous) and that's still cutting it close. Welcome.

Next, read my post "How to Freelance" which explains how I built a network from scratch in NYC and now make a great living at the same time.

Good luck!