The cute Beastly Kiosk at Animal Kingdom is located directly across from the Adventurers Outpost on the walkway between the Tree of Life area and the Asia section of the park (just before the bridge that leads to Drinkwallah).
The Baked Lobster Macaroni & Cheese from Animal Kingdom's Beastly Kiosk.
Viewing the Beastly Kiosk looking north-west you can see some limited seating to the far right of the booth.
There are a few seats near the Beastly Kiosk. These are more likely to be shaded in the afternoon. While the tree canopy here is pretty dense I wouldn't call it "covered" seating.