Walking is the greatest way to get to know a city.
There is no other way for you to see things you would have never seen before, and get to know somewhere from the ground up, and the recent rise in popularity of "Free Walking Tours" is a big piece of evidence for that.
Walking tours are now featured in mainstream travel articles like this one from the New York Times, and as such, walking is getting the attention it has always deserved. Though some people might argue for the advantages of segway-ing, the über-basic transportation of walking is king for getting to know your surroundings.
(Photo from http://www.eltelegrafo.com.ec/noticias/cultura/7/el-caminar-un-detonante-para-recuperar-el-espacio-y-el-cuerpo)
As reported by above professor and walker, Alex Schlenker, walking itself is a way of making culture and creating your own space in a way that maps can't show. Walking creates an event where you can be yourself in a new, beautiful space, and add your voice and actions to a place, while also letting the place affect you in a way that can cause a sense of awe or wonderment that creates a strong bond between people and places.
While looking at a map tends to show you helpful things to know, walking forms a different imprint on your brain, and creates experiences that not a map or car ride - not even an afternoon on a segway - ever could. The helpful places that maps tend to share with people - apart from the physical spaces themselves, are often times based in some sort of capital, impersonal gain for the place.
While walking, the pressure of getting somewhere and experiencing what you expect to experience in that specific area based on stories you've heard about that place or marketing about that place dissipates, because you always are somewhere. You're already walking, which was the goal in the first place.
And you really never know what you might find on a walk. Sometimes, you might even feel yourself wandering.