I agree with staying on site at a moderate. Maybe the Port Orleans and French Quarter. I am assuming they will not have access to a car while you are working. It would make it really easy for them to get around using their bus system. They could have lunch at Downtown Disney and stuff.
If you are looking for more budget rates, check out the Country Inn and Suites or Amerisuites at Calypso Cay. They have a small zero entry pool, a small waterslide, mini golf, free breakfast. They do not have a restaurant on site and I don't think there are any in walking distance, but we did have pizza delivered there. You could probably find rates between $60 and $80 a night.
If HIFS is in the budget, it is a very nice place for kids. They only thing that kept us from going back there was the lack of the slide. Now that they are planning on adding them, I am sure we will be back.
Liki Tiki Village has a small waterpark geared toward younger kids, and they have one and two bedroom condos. You can usually book the 1brs for $89 to $99 a night. They have not gotten good reviews on these boards, though. We have never been there, but the water park looks pretty cool in the pictures.