For almost the same reasons, Chad and I are thinking of relocating to Austin. $1800 for a 700 1 bedroom is awful, and rent will be going up next year. Ugh.
My advice, though, is to wait to buy a car. Otherwise you'll have to pay double the fees (fees to NY when you purchase and then fees to PA when you move). If you can, definitely wait.
As for the moving time frame, that's completely up to you. You can move out next week if you want too, but you won't be prepared.
Start looking for work first. Many places will do interviews over the phone. Then, once you have something secured, look at apartments in your new pay range.
SAVE! SAVE! SAVE! Cut back your spending as much as you can. Buy essentials and buy in bulk to cut costs. Being single, it may seem daunting but you won't have to buy again next month. Or possibly until you're in your new place.
That's what immediately comes to mind. Good luck to you! What an exciting time.