If you gained your PR through a PNP, some people may tell you that you must live in your PNP province for a certain amount of time, until you get citizenship or possibly even forever but this is not true. There is no law that says that you do. After you get your PR, you are free to leave. However, if you are a PNP applicant, you should not have planned to leave before you land or you might be guilty of misrepresentation since it is the requirement of PNP that you intend to settle in your PNP province.
After moving to another province, your SIN is still valid but you need to inform the health care at your old province that you moved and you need to register for health care in your new province. Your old province health care will cover you while you wait for the new one to kick in. You will also need to exchange your old province drivers license for a new province drivers license of the same class and this will not be a problem either.