You have to put yourself in their shoes for a moment and think about what their impression will be of you and what they think you will do to their yard. I always introduce myself with a handshake and a smile. It makes a world of difference. I try to quell their fears that I'm not going to leave mole holes all over their fine trimmed lawn and explain that I only cut plugs or trapdoors and I replace all my divots. You have to always remember that if you are given permission, you are a guest in their yard and should behave accordingly.
Yards are a good place to start, but they're only the tip of the iceberg.
The possibilities are endless. I found four old silver dimes this spring on a boulevard in the street. Campgrounds in older areas are usually productive places to detect, especially if the ground has been used for recreation for many years. Almost every campground I've visited had a set of rules and if metal detecting is forbidden, it will most likely be clearly stated. Federal land is another ticklish place to detect.