Non-netted outdoor orangutan exhibits can be found at many American zoos. Here's a partial list: Philadelphia, Busch Gardens, Miami, Tampa, Atlanta, Memphis, Audubon, Oklahoma City, Gladys Porter, Fort Worth, Houston, Indianapolis, Kansas City, Phoenix, Denver, Hogle and Woodland Park.
In Mexico : The Guadalajara zoo , Leon zoo and Zacango zoo all have non-netted outdoor enclosures for orangutan (The first two being far better than the latter). Chapultepec zoo has a pair of netted / enclosed exhibits for their remaining orang , Toto.
If you want to seen an overall list of orangutan facilities in North America you can check out the topic in the North America channel.
This yard is pitifully small, but it does have one redeeming feature--a high tower that the orangs can climb to brachiate across the "O Line," which the animals can use to traverse the distance of two buildings high above visitors' heads to the old Monkey House. Called Think Tank, there they can play computer games/research for food rewards and stay overnight if they wish. So, the orangs are actually encouraged to "escape" vertically, the very antithesis of mesh containment!
Como in Minnesota is one that is unnetted as well. Chahinkapa in North Dakota isn't netted, but is surrounded on all sides (including the top) by bars.
No, it's essentially netted. To be fair it's solid wire instead of netting, but the function is basically the same.