All Disney resorts are kid-friendly. The most affordable onsite resorts are the AllStars. However, booking just one night can be difficult. Disney has an algorithm that they use in order to ensure that rooms are almost constantly in use. It makes single nights are hard to come by. Check the disneyworld.disney.go.com website for prices and availability for the night you're looking for.
I'd recommend looking at Hotwire and Priceline Express deals to see if you can swing something there. Most are built for families so it's just a matter if you want to pay Disney the higher prices for the on-site perks or not.