This tiny camera capable recording 1080p30 can be found for $59 on Amazon.
There is also an improved version of this cam - Cube Plus (Cube+) which is based on more advanced AIT8427 chipset and can record video in 2k60 (1440p) and 720p120.
Polaroid Cube and Cube Plus firmwares: Cube Cube+
Is also an AIT8427+OV4689 hw platform solution.