My two cents:
For small children, I would recommend Bay Lake Towers. It has direct Monorail access to the Magic Kingdom. There is also a short walking path from BLT to the Magic Kingdom if you decided to walk. Because of your small children the Magic Kingdom most likely will be your most popular park.
Chef Mickey's is also close by in the Contemporary Resort. Contempo Café, Cove Bar, Sand Bar are counter service restaurants. There is also The Wave and California Grill (signature.)
Animal Kingdom Villas is a great resort too. It is the most themed resort, and the animals, activities, pools, water play areas are wonderful; it is a vacation within a vacation. It is an experience waking up to giraffes outside your balcony. The only draw back is it is further than the other resorts and transportation is the Disney Bus System, which sometimes people complain on the wait. If you are driving your own car or do not mind the inconvenience, you should be fine. We personally have not had a problem with the bus, but I have read complaints.
If you are staying at Kadani ( Animal Kingdom Villas), eating choices are very limited, however "Sanaa" is a very good restaurant with views of the animals. There is also transportation between Kadani and Jambo House (Animal Kingdom Lodge)where there is Mara (counter service) Boma(buffet) and Jiko restaurants, a signature restaurant.
Wilderness Lodge is a popular among many families. It is a beautiful resort, has a great theme, plus uses boats or buses to the Magic Kingdom. The bus system is used for all other parks. There are also nice family choices to dine, Whispering Canyon, Roaring Fork(counter service) and Artist Point (a signature).
There are other Disney Resorts: Saratoga Springs, Boardwalk Villas, and Beach Club Villas.
However, if it were me I would choose 1. BLT 2. Wilderness Lodge 3. Animal Kingdom (only 3 because of distance, but a toss up depending what you want) the theming and animals are very cool, plus the rooms are very nice and also themed.
What ever you choose I am sure you will have a great time! Good luck!