The first several caches I found were out in the woods and I didn't feel weird or anything. When I started doing more urban caches I did get a little uneasy at first but I've gotten over it.
I'll set up a series of caches I want to do as a bookmark list, create a pocket query, and dump it through GSAK. As I go through the caches in the field if I come up to one that may be over run by muggles or what not I'll make notes and flag that one for a come back later.
As for the looking suspicious around playgrounds and parks, walk your dog if you have one. Also works in other areas to like parking lots and convenience stores. We have found this to be effective. Because single guy walking around in park might look odd, but with a dog people are more likely to disregard you because you have a reason to be there. We have pit bulls and dobermans which helps out also. They don't have the cute, cuddly, and "can I pet your dog" appeal other breeds have. People will see us but they also will give us a wide berth