I think this is a case where having a dog with you could come in handy Assuming it's a 'dogs-allowed' area of course.
I've found that no one pays attention to you/what you're doing if you've got a dog with you, unless they want to ask about the dog. People with dogs are just somehow less suspicious!
Example, there's a suburb near my house without sidewalks on the sidestreets, and pretty much no one who lives there walks. I go to the area with friends to get ice cream during the summer and we often walk around the neighborhood to eat it. If we have no dog, people look suspiciously at us. If we are walking a dog, they just ignore us.
I've also found this it true with police officers-- they tend to be less suspicious of people with dogs... I remember when I was young enough to be under city curfew laws a friend and I used to walk around way past curfew a lot. We always had our dogs with us though, and none of the police passing ever bugged us, except once or twice to wave and smile at the dogs!
Aside from simply walking WITH a dog, having one can also be useful in that if someone catches you searching for a cache you have more things to make up such as you're looking for your dog's lost tennis ball