We had a nervous 7-year old who really loved the kids area at BB. His older siblings were all over the rest of the park, but he took it easy at first and there were plenty of cast members to help him out. After an hour or so in the kiddie area, his siblings convinced him to try some of the more 'grown up' attractions.
One tip: go early, first thing if possible. The kids will get lots of personal attention, and by noon or so you'll all be ready to head back, with plenty of day left. Have fun!