Here is a link to the standard conditions of probation, Eastern District of New York:
http://www.nyep.uscourts.gov/html/conditions_of_probation.html
The defendant "shall not leave the judicial district without the permission of the court or the probation officer."
"Shall not" is an order not a suggestion.
It appears your attorney worked to get you a plea that keeps you out of jail until your sentencing on your felony charge. The probation you were granted can be revoked if you violate ANY of its terms.
You are already looking at jail/prison time. It is a mistake for you to ignore the terms of your probation because the court will likely not look on you favorably if you do. The judge is more likely to sentence you to the maximum allowed.
Please rethink your plans to move without authorization. You are already concerned about "screwing up" your life. An unauthorized move is one way to screw it up more. Your new residence could be in a new city if you follow through with your plans but your new accommodations might include bars.
Good luck.