Hi Michelle!
In general, Disney resorts do not allow pets of any kind with the exception of the
Fort Wilderness Campsites. It is very hard to determine which resort would handle a service dog better then another.
I am assuming your son will be with you and you will be the sole person in charge of the walks and relieving times. The first thing I would do is request a first floor room in a resort and not a higher floor. This will let you simply open your patio door or room door and head to find a good spot. Please remember that since Disney resorts are not dog friendly it is important you bring your own bags to clean up after the dog as nothing will be provided.
Also understand that some guests will be afraid of dogs and will not expect to see any during their stay. Being a service dog I know how well trained they are but keep the vest on so it is visible for the guests to understand its role and duty for your son when he is not with you.
To me the perfect location for you to stay while on your vacation is the
Fort Wilderness Cabins. They are quite roomy with a separate bedroom and tv, a large bathroom, a fully equipped kitchen and dining, and a queen size pull out sofa bed and large screen tv in the living area. Outside there is a deck with picnic table and grill. They have handicapped cabins if you would be more comfortable in those. The best part is that your cabin is completely private and surrounded by lots of grass and /or trees so it is easy to walk and relieve your dog. I can imagine that after working hard in the busy parks the dog would love the peace and quiet of this wonderful resort. You can rent a golf cart as well so getting around is fun and easy.
Hope this helps you with a decision!