Any way to recover photos from a restored iPhone? I accidentally restored my new iPhone 6+ (iOS 9), which didn't have iCloud enabled, from an old backup (iOS 8), with iCloud.

My important photos seem to be gone now. Is there any way to recover photos from a restored iPhone?
Since you didn't link your photos to anything online, you may be able to go to a data recovery specialist and ask them to try to recover the photos, but it probably won't work (Depends on how large your backup is). 

If you don't do that or that doesn't work, then you can't get your photos back anymore.