Drive with open doors
In the garage, modify your car and go to the "Doors" selection to preview the door opening. Once it opens all the way, back out and then immediately press A as soon as the menu appears. Your doors should now be stuck wide open. They will close if you select some options, mainly the "Doors" modifications. When you leave the garage, your doors will still be stuck open, and you can drive around with them in this position.