Specifically, Bloomberg has "issued an executive order requiring city agencies to promote the use of stairways and use smart design strategies for all new construction and major renovations." Going forward, more areas of New York City will have more staircases, and you will walk up those stairs more than you do now. You will, perhaps, take fewer elevators and escalators. You will climb a greater total number of stairs in your day to day life in New York City than you do now. Will this get you "in good shape?" No, it will not.
Look. Let's level with each other here. Yes, walking up a flight of stairs is better for you, physically speaking, than taking an elevator. You expend more calories climbing a flight of stairs, yes. But the gains that you will make from doing so are negligible. Taking the stairs, as a habit in the course of your day to day life, will make you more fit in the same way that stopping to pick pennies up off the ground will make you more rich.
Let's see here... "A 150-lb person must climb stairs for 6 hours and 30 minutes to burn the amount of calories in 1 lb of body fat." My friend, you are not even going to come close to that. Even if you are a very enthusiastic adopter of Hizzonner's "climb the stairs more" proposal, you are going to climb the stairs maybe, oh, an extra two minutes per day? So, if you keep everything else in your life exactly the same, you should be able to burn off a little less than two pounds a year. Meanwhile, a quarter of our fellow New Yorkers are clinically obese.
But of course you won't keep everything else the same. You'll reward yourself for taking the stairs. A few ice cream sundaes, and that entire caloric gain is shot. You also won't be really working to go up the stairs. You won't be sprinting up the stairs at full tilt. You'll be ambling on up those stairs, slowly. This is not a workout. This is normal functional human movement. "Taking the stairs more" is a prime example of an an activity that people are told to do that will make them think they are engaged in "exercise," without really offering them the benefits of actual exercise. If you are interested in climbing stairs as an exercise to gain true health benefits, you should be sprinting up and down the longest staircase you can find, dozens of times per day. Or at least entering that race up the Empire State Building.