Visitors see a city that residents don't. They look up, they read plaques, they get lost on purpose, and they go to the obvious places that locals have decided are for tourists. After a few years in a place you know your routes and almost nothing beyond them. The good news is that exploring your own city costs nothing and needs no time off work; it's a matter of looking at it as if you'd arrived this morning.
The ideas below are in four parts: the tourist test, going where you never go, learning to look at a street, and a half-day itinerary you can run this weekend.
Ask what a visitor with one free afternoon would do in your town, then do exactly that, without irony.
A city is mostly the parts you don't use. Residents carry a surprisingly small map in their heads; a visitor has none, which is an advantage.
Visitors notice details because everything is new. You can borrow the trick by looking for one specific thing at a time.
Here is a Saturday morning, assembled from the above. Start at the station or the central square and find the map board. Pick one thing on it you've never visited and make that your destination, ideally across whatever divides the town. Walk there through the oldest streets, looking for one detail from the list above per block; don't hurry. At the destination, find the nearest water or the nearest high point, whichever is closer, and spend ten minutes there. Then walk back a different way, through a neighborhood whose name you've never said aloud, and finish with a coffee somewhere you've never sat.
Four to five miles, three hours, and you'll have been to at least two places in your own city for the first time. Do it once a month in a different direction and in a year you'll know the place better than most people who've lived there all their lives.
The thing that makes this stick is a record, and the best kind is a map that shows you not where you went but where you still haven't. That's what RLQuest's explorer map does: the city is divided into hexagon tiles about 350 meters across, and tiles fill in as you walk them. After a few months the blank ones are the honest picture of your own town, and the morning quests nudge you toward them: uncover five new tiles, find four on the side of town you rarely visit, reach three on streets you've never walked. Other quests lead to real places, towers, old gates, viewpoints, ruins, drawn from OpenStreetMap; be the first in RLQuest to complete one there and it's logged as your first find. The app checks the recorded route and the tiles, and it stores which tiles you uncovered, not where you were.
It's free to download for iPhone and Android, with a Premium subscription that adds more quests per day. The itinerary above needs only shoes.