When are you planning to go? It's possible that you could stay at a resort near the Magic Kingdom for about the same price as a moderate resort. Disney has a timeshare called the Disney Vacation Club (DVC) based on a point system. Members can book a villa at special DVC resorts at WDW and the villas cost a certain number of points depending on location and time of the year. A studio villa would be perfect for you. There are DVC resort villas at
all the Magic Kingdom resorts (the Grand Floridian, the Polynesian, the Contemporary and the Wilderness Lodge). You can look here for more information about renting points:
http://www.disboards.com/forums/dvc-rent-trade.29/
If you don't want to rent points, I concur with Port Orleans French Quarter if you want to stay at a moderate.
I also think that your son would LOVE the value resorts if you want to save some money. Yes, they are a little bit out of the way and will add a few minutes to your "commute" to and from the parks but like
@disneyvoice says, the savings between a value and a moderate will pay for a lot of fun things to do in the parks. I wouldn't discount the values because they are not close to the MK.
I agree that you should take an umbrella stroller with you. Some people are park commandos and go-go-go all day. We have always taken a break for a nap and a swim (even now with a teen!). If you think your son might melt down after a few hours you can always plan in a mid-day break and then go back into the parks for the fireworks.