But what can I do with my insurance from another state?
If your coverage time haven't lapse you can still use it there. Whenever you go to a different state, that you have an insurance in, DMV will cover you there. So, if you ever go back to that state your insurance will still work.
If my vehicle is registered here in new york, would that be a problem when I visit another state I have a insurance in?
If your vehicle is registered in New York, it MUST have a New York insurance. If you go to texas (where you have a Insurance coverage) you'll have to first register the vehicle there, in order to be able to use their insurance.