Amazon has the Hohem 3-Axis Gimbal Stabilizer for GoPro Camera for $99 - $20 off with coupon 20OFFPRO2 = $79 with free shipping. Features 360° panorama, rechargeable 4,000mAh battery that also functions as a portable battery pack, motion time-lapse.
Has good Amazon Reviews.
eBay has the Remo+ DoorCam WiFi Smart Over-the-Door Camera, (DCMU-1706) for $99 with free shipping. List price: $199. It fits over your door and features a 160° field of vision.