I'll agree with loins and backstraps but a lot depends on how you plan to cook it. I used to let the dogs eat the shanks until I slow-cooked some (low heat, 8-10 hrs.) in the oven. The meat slid off the bone and was very tender and tasted great. Now I cook shanks and other gristly cuts in a crock pot. If you do that with a good cut like a backstrap, it doesn't turn out as good, because the collagen (connective tissue) in the shanks turns soft with slow cooking, and the good cuts don't have much of it.
My son's girlfriend doesn't eat much meat but she'll eat the elk I cook. Her favorite is the stuff I cook in the crock pot.
