First you should check Turo.com as there are private owners who will rent their car. That is a good way to really get more intimate with the car, though be careful of the mileage limits. And of course make sure to find out if the vehicle you rent has AutoPilot (and if so, V1 versus V2).
Beyond that, you may be able to get an extended test drive from a local store, but that will depend on the specific store and what they have and how long they can be without. My local store allows overnight on occasion, but not a week long road trip or anything quite that extensive. Good luck!