Before we bought our timeshare, we rented single homes with our own private pool. We rented many times thru
www.villadirect.com and had a great experience each time though many disers will say to avoid them.
Their homes were always exactly as shown in the photos and were always decorated beautifully. Many have big screen tvs, garage converted to game rooms with air hockey, billiards, foosball, etc.
Once you have that much space and privacy, it's awful going back to a tiny hotel room with 1 bathroom.
Here are the neighborhoods that are closest to Disney:
Formosa Gardens
Indian Creek
Rolling Hills
Windsor Hills
Windsor Palms
Emerald Island
These are all near Formosa Gardens Blvd. in Kissimmee if you want to Mapquest/aerial view. (southwest of Disney)
There are many newer areas on Rt. 27 but it's a longer drive to Disney and even further to Universal.
Unless you're going in summer, I'd recommend paying the extra for pool heat. It's heavenly to swim at night after a busy day in the parks.

The one time we didn't get it, the water was freezing at night.
We're not ones to order room service and we really don't care if the beds aren't made when we return so it's a no-brainer for us but some like more service so they prefer a hotel. We also don't need to be "immersed in Disney" 24/7 and enjoy the quietness of being offsite. ymmv.