The benefit of running outside is that you're presented with endless reasons to explore your own city. Here in NYC, we're exposed to a variety of landscapes and neighborhoods that are just begging to be discovered and if you live here, I definitely encourage you to take advantage of it! From the Hudson River greenway, to the East river paths, to Prospect and Central Parks, not only will we be taking in all the views that NYC has to offer, but you'll also be hitting a variety of terrains and elevation that can help you improve your running.
Once you start running regularly (about 3x a week for at least a month or two) you might get to the point where you'll feel ready to push yourself to the next level. There are two things you can do to challenge yourself to build up strength and speed: hills and speedwork.
Hills: There's nothing like the hills of Central Park and Prospect Park to improve leg strength. Two tips I can offer for tackling hills is to shorten your steps and slow down your pace. If you're nowhere near NYC or areas of elevation, don't rule out bridges. These are also great opportunities for incorporating hills into your workout. I'm a huge fan of the Williamsburg and Manhattan bridges (free of tourists!)
Speedwork: When you've got a flat course like the Hudson River Greenway or the East River Bikeway on your workout agenda, use speedwork (or interval workouts) to train your muscles and heart to help you run faster and longer. Out of the tons of workouts available online, try to find ones tailored to your present ability level and goals. But be careful with jumping into speedwork: it's an advanced training technique for intermediate-advanced runners and without the guidance of an experienced coach, can lead to injury.
Do you incorporate hills and speedwork into your runs? If so, where and what goes into your workouts?