Hi, Josh! The closest resort to the Magic Kingdom is the Contemporary Resort. This is the only resort within walking distance to the Magic Kingdom. Other resorts that are just a monorail ride away are the Polynesian and Grand Floridian.
Of these 3 resorts, all in the
Deluxe category, I think the Polynesian is your best choice with little ones. There is a zero-depth entry pool, a fun beach, and great views of the Magic Kingdom fireworks from the beach. From the Polynesian, you are also within walking distance to the Transporation and Ticket Center where you can catch the Epcot monorail.
If you choose to go with a Value or
Moderate Resort you can take the Disney bus transportation to the parks. These resorts are not as fancy and not as close to the parks, but are all family friendly and budget friendly! Buses run approximately every 20 minutes.
Check out the different resort options and pricing and find the resort that will be just perfect for your family!