On board camera.
 

I have nice little battery powered HD camera that weighs 4.4 oz. I'd like to mount it to my Tower Trainer 40 just for recording on the SD card only.. Any advice appreciate. Location. Never done it before.

I mounted a go pro to the gear on my 40%er. But that is a big difference than a trainer.
Youre going to see the prop but I'd mount it on the spar. Perhaps with Velcro and tye wraps

If you want a pilots view then mount it in front of the windshield or on the center of the wing.
If you don't want to see the prop then go to the left or right on the wing. As mentioned keep it on the spar . Plus don't go too far to the end of the wing without adding equal weight in the same spot on the opposite side of the wing.

If the camera has a mount then secure that to the plane . If not then just mount the camera using some good quality velcro.

I'm thinking under the fuse, between the landing gear for best CG position? Seems simple enough but want to make sure I'm not missing something important​.

Keep in mind that some cameras can't flip the image if you mount them upside down. You would have to flip it after in moviemaker or another video editor.