Much of the answer to that depends on personal preference and budget. I can offer a few suggestions and then you can decide which resort would best suit your family.
A very convenient (but equally expensive) option for families with young children (and multiple strollers) would be a stay in one of the monorail resorts. There are three of them: the Contemporary, The Polynesian, and The Grand Floridian. Of these, I think the most playfully themed option would be the
Polynesian where they have a volcano themed pool and a Lilo and Stitch character breakfast. Any of the monorail resorts, though, would make trips to the Magic Kingdom quick and oh so easy.
If you aren't looking to spend quite that much on your accommodations, you might consider a stay in the
Fort Wilderness cabins. Each cabin can sleep up to six (plus a child under age 3 in a crib) and features a full kitchen, a separate bedroom (great for napping) and curbside parking. If the kids in question are outdoorsy types then this option might be a great fit for your family.
For the most budget conscious traveling families, Disney provides larger-than-life theming at the All-Star resorts. Children seem to be especially partial to the
All-Star Movies resort where the characters from Toy Story and 101 Dalmatians greet you in humongous fashion. Your group could get multiple rooms at any of the All-Star resorts or you could opt for a few family suites at the All-Star Music resort. That choice would give you the benefit of multiple bathrooms and separate sleeping areas.
Good luck with your planning!