Hi Cori!
As you said there are family suites at the
All-Star Music Resort. Depending on what your needs are, a
cabin at Fort Wilderness might also work out. However, if you consider either of those then you should also consider just getting two connecting rooms. It can be less expensive to get two connecting rooms at a Disney Value or Disney Moderate Resort.
More expensive options include a Deluxe Club Level room at the Wilderness Lodge and 1 and 2 bedroom rooms at a Deluxe Villa Resort, which is the Disney Vacation Club (DVC) portion of a Deluxe Resort. My favorite DVC resorts are at the Wilderness Lodge, Animal Kingdom Lodge, and the Beach Club.
Another option is a hotel with a suite at Downtown Disney. My family has stayed at the Doubletree Guest Suites in Downtown Disney many times and have always enjoyed it. However, you should know that while it is in Walt Disney World, it is not a Disney property; the Disney buses don't run there and guests staying there do not get to enjoy Extra Magic Hours. However, the hotel does share a bus with other Downtown Disney hotels.
Enjoy planning and write back if you have any more questions!