Too often, when people ask for "local" they don't really mean "local". I have stayed at the Acapulco Princess Hotel and there are two delightful restaurants on the property. The cab ride is fun (about 15 - 20 minutes tops) each way. After you dine, check out the grounds - beautiful.
If you would prefer to remain in town, then a good "local" restaurant is Sanborns. I've eaten there in Acapulco and also at their restaurant in Mexico City. It has been in existence at least since the '40s. You really can't go wrong.
I could recommend a couple of others but they really are LOCAL and I don't think you'd be ready for them - or vise-versa.