I've been taught to "store" the prayer rope in one of two ways...
One way (the most common i've seen) is to wrap it around your left wrist.
The other way is to wrap it around your belt... If I do this, then I tuck the rest into a pocket.
However, I try to avoid putting it completely in my pocket, especially because it is so easy to forget it's there, even when hung on a belt. If I am wearing long-sleeve shirts, I try to wrap it around my wrist so that I remember it's there.
That in combination with an Orthodox cross on my neck (usually I wear it outside my clothing, depending on what clothes I'm wearing), it helps to remind me who I am and what I'm a part of, and it helps keep me "well behaved". It also offers a good opportunity to "witness" to someone.
However, it is NOT to be worn as a form of decoration, nor out of pride. It isn't jewelry or any decoration. In my opinion, this is the same as your cross on your neck (if it's your baptism cross). It's not for show.
Here in Greece, it's much more common to find people with prayer ropes that are already small enough to wrap around your wrist automatically. I don't know if they use them or it's just decoration. But it's definitely less "showy" than having a 50-100 knot rope around your wrist. But then again, I rarely see Orthodox here wearing the prayer ropes with more knots. (unless they are clergy or monks)