I believe that in order to really see the world when you travel, you sometimes have to throw away your map and get lost. Lose yourself in the experience and not only see the tourist sights.
There are many ways to do this, many things that can inspire you to find and see other things, places and people. I like the Anywhere Travel Guide, it's filled with cards with tips about how to see other stuff. Like this one. I'm doing that the next time I'm somewhere new.
But off course, ute common sense when doing this. You don't wanna be a stalker:)