One group that is underrepresented in zoos are small passerines. Even though many of the estrildine finches of Africa/Asia are often fairly well represented in private hands, they are very rare in collections. For a lot of these a walk-through set up similar to a butterfly house might make a good exhibit I think. The only thing rarer are the small passerines of South America - I have never seen any of these in a European collection at least.
San Diego Zoo and the Safari Park do reasonable there in my opinion. I remember seeing a lot of estrildids, tanagers, emberizids, weavers, and leafbirds. I also saw chickadees, thrushes, laughing-thrushes, bulbuls, robin-chats, leiothrixes, and whydahs. I missed Bearded Reedling, Cedar Waxwing, a smaller cotinga or two, and some other unusual species. They now have at least one species of sunbird on display as well.
The smaller section of Hidden Jungle at the Safari Park is similar to what you suggest, and had a good number of estrildid species as well as a few other birds. Overall I rather enjoyed watching all the little finches.