Still in the very early exploration stage here. If we DID stay off-site, I'd have to price the cost of parking and car rental vs staying on-site cost. If we did have a car, how difficult is driving into the parks/parking, etc? Are there long lines? Traffic jams getting into the parks or out of the parks? Do you park really far away and have to wait for shuttles? Or walk super far? Or is it all pretty easy? I have no idea what having a car is like and I don't remember even really seeing parking areas...or I just paid zero attention to them.
We generally rent a car even when staying on site. I just don't like the busses so the added expense is worth it to me. Driving to HS, Epcot, and AK is easy. There is some walking but not much. Plus you are at Disney where you are walking 30,000 steps a day anyways. Parking for MK is very much a no thank you because you park at the TTC. The lines for the monorail and ferry can get very long.
Keep in mind if you do stay off site and rent a car you have to pay for parking. If you stay on site and rent a car you don't have to pay to park at the parks but you DO pay a daily fee at the resort. Either way they get money out of you for having a car.
I’ve driven my own car in several times and have never found the lines to get in or the shuttles be too bad. Sometimes there’s a bit of a walk from your car to the shuttle line, though.
Like PP said, you may very well have to pay for parking at the hotel anyway if you stay on-site, so you really get around paying for parking either way.