Always Have A Map — But Don't Be Afraid To Not Look At It
First of all, ditch the paper map. No one wants to look like a lost tourist. In exchange, either use Google Maps or, even better, download map apps that don't require Wifi. Then, forget you have it. Let yourself wander and if you get lost, you can turn to your map and find your way home again. Or wander forever. It's your call.