I would walk around downtown and enter many public buildings and listen to what people are saying. I might try and see how my friends are really doing. I would sneak a peek at how they're teaching kids in school, and how the kids are responding ( yes, I would really do that). I would love to over hear two of my ex-girlfriends talking. I don't think, even being invisible, that I would abuse that feature.
I think I would not like to be invisible for too long. I think I would prefer to be able to fly. that sounds better.