If it's a military post, the local Provost Marshall is the person to ask. Churches, older school yards, and ball parks are great places. I've found some of my best coins and nicest relics in them. Getting permission to hunt a church yard usually just means asking the pastor. He'll either give you an answer or turn you on to someone who will.
Schools are another story.
I've never had anyone hassle me about hunting on public school grounds. The thing that makes schools such a lucrative hunt is that kids will lose anything. Getting a place to start detecting is not as hard as you would imagine. Just look around.