Amazon has the ASUS VivoMini UN62-M036M 4th Generation Core i3 Mini Barebones Desktop Computer (No OS) on sale for $200 - $50 rebate [Exp 06/30/2017] = $150 with free shipping. Newegg has it for $153 shipped after rebate.
Supports 4K UHD and Windows 7 through 10. Measures just 5.15" x 5.15" x 1.65".
Intel Core i3-4030U 1.9GHz, no installed memory (16GB max), no storage (supports mSATA SSD) Intel HD Graphics 4400, Gigabit ethernet, 802.11ac, Bluetooth 4.0, 2x USB 3.0, HDMI, DisplayPort