Waistband is the place to put it. Some running shorts come with a waistband pocket, in front is ok but in back is what I prefer. You can also get… A waistband with a pouch is the best way to describe it, just big enough for a phone and keys pretty much and you can put it under your clothes easily
Not quite the same thing but I always worry people think I’m shilling when I talk positively about a product.