No, you will need to buy your policy where you permanently reside, not where you drive.

You will have to have a valid license and obtain vehicle registration in that state as well. Even though you travel to Illinois frequently your state of residency appears to be New York. If that is the case and that is where the vehicle is titled and registered, then you will need insurance in New York.

When insuring your car, remember to get a New York insurance quote from CarInsurance.com!