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When building a desktop PC, I usually don't list a case because they are very personal to the user. However, when it comes to all-in-one systems, the chassis is all important because this is both the display and the home for all your components.
For this build I've chosen the Loop L5 LP-2150 chassis, which is based around a 21.5-inch display with a resolution of 1920 x 1080. It supports thin mini-ITX motherboards and LGA1155 processors up to 65W TDP. It features two USB 2.0 ports, and has integrated speakers, a microphone, and a front-facing camera.
There are many others you can choose from, and if you are interested in shopping around, I suggest you take a look at Intel's Design Component Catalog for inspiration.
Image source: Loop.