So long as you are not on probation, I would imagine that this would, in fact, be the end of the case and you would be free to go about your business. Given the charges you faced, I'm sure you must have been appointed an attorney if you did not hire one on your own. Be sure to address these questions to him/her at your court date, if not before.
This response is for general purposes only and does not establish an attorney-client relationship. You should contact an attorney to fully discuss your issues.
You should know the answers to these questions prior to entering into a plea agreement. If you have an attorney, and if plea negotiations have taken place as you describe - you must, then you should discuss this with him or her.
If all you are not getting put on probation, then your case will be closed as soon as the judge accepts your plea and you are sentenced. Then you will be free to go wherever you want without restriction. However, if you are put on probation then you must first get permission to go back to New Your from either the judge or probation or both. It is best to address this prior to or at the same time as your plea hearing to get everything on the record. Talk to your attorney about it before court. If you don't have an attorney, get one immediately. Good luck.
You should have an attorney and you should be asking your attorney these questions. It depends on the judge. Some judges want for you to be put on probation and would order for your to get a pre sentence investigation report prior to sentencing. It does not sound like the DA is requesting that. However, the judge ultimately decides.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice. Mr. Leroi answers questions on Avvo because he strongly believes in public service from his years as a judge, magistrate, and prosecutor. If you need to ask any follow up questions because my answer did not fully address your question, feel free to call Chris or post an additional question. Thank you.