I just returned from a week in Orlando and I rented an
ECV for the duration of my trip. It will be far cheaper to rent one yourself rather than trying to get them at the parks each day (UO charges $45 a day, but mine was $30).
The more reputable
scooter rental companies deliver directly to your hotel and will pick it back up there too.
Make sure you look at the videos on the various Web sites for the rental companies. I had looked at them for a few of them, but booked with a company (Walker Mobility) whose videos I didn't watch. Didn't know until we were done with it the first day that the steering column didn't fold down and that we had to bring the entire thing (not just the batteries) into the room each night to recharge it. Four times a day, we had to dismantle it/put it back together to lug it in and out of the trunk of the car. It did take up most of the trunk of the car, so keep that in mind if you're getting a rental. You need a big trunk or something with a hatch.
Walker was good and the scooter was fine, but I personally won't rent with them again because it was a pain to deal with the assembly so much. Don't forget to rent a canopy too -- kept me much cooler!