With a bow and arrow, we aim for the wing butt on a side shot. I’ve heard a good round ball shot is right through the beard on a gobbler, when facing toward you. It spoils less meat, because the ball exits the back. If you’re really good, and the turkey is close, aim for the eye.
Here in Pa it's shotguns only in the spring but fall turkey can be taken with a rifle. I've gone fall turkey only once but didn't like it because I had to share to woods with small game hunters and archery deer hunters. I do know of a guy who took one with a .36 caliber. Turkey dropped in its tracks.
I wish they'd allow rifles in the spring but I see their logic as it's a safety issue with the spring foliage.
I've taken several Toms with a roundball. You can go down to "The Hunting Journal" page and read about my last one "40 caliber gobbler". I shoot them in the wing butt or right where the wing attaches to the body. It leaves a tidy .40 caliber hole all the way through. The turkey might go a few yards but he won't go far. Hunting with a decoy and a Tom that holds still at close range, it is certainly possible to take a head shot. But out in the shadows it is still iffy and I like to kill what I'm shooting at. So it's the wing butt for me. Download a couple of turkey sillouhettes with the internal organs shown and learn how they fit together and where to aim.
I have had very good luck with front facing shots placed at or just slightly above where the neck meets the body, both with a .36 cal roundball and with a modern crossbow. It takes the fight right out of them. The "hit 'em high watch 'em die" adage has held absolutely true in both cases.
Here's video from a couple of years back with my Tip Curits .36 cal flinter on a PA hen during their Fall season to demonstrate:
Wish I could use a roundball for turkey out here. For archery, I imagine a line going straight up from the legs & slightly forward. Check some archery forums for shot placement tips. While hitting them low could end up gut-shooting them or just hitting the keel (assuming you're a little forward of the legs), too low and you take out the legs. A turkey can run without wings. But he can't fly or run without his legs.