kids that age. I would stay on the Monorail if you can. If you have a military discount - perhaps Shades of Green.
This REALLY comes down to availability and budget.
1 - Monorail hotel
2 - Wilderness Lodge
3 - Epcot area resort (if you are doing epcot / Studios). Yacht / Beach / Boardwalk.
If your budget is like most (and me). Try also the SWAN / DOLPHIN. They aren't as "disney" as you may like - but they are less expensive (however parking is $20 / day) and the location is great.
As you go to moderate / budget - the convenience goes down a bit - but as you are FL - I assume you would have a car.
If you are doing all parks - there will not be one area that is most convenient for all. But in reality - none are too far away.