When I go to a new city, I find a landmark than take the train/bus/subway towards it but not to it. I get off ~ 3-5 miles away from it, then I try to find on my own navigating the streets in the general direction of it. Yes, it takes a an hour or two to get there, but I get to see things at random which otherwise I would miss.
I have seen people with phones in their hands asking for directions and not knowing how to tell Google Maps where they want to go.