The standard directions for how far off the floor a towel ring stand should sit is 42” to 48”. Depending on how tall your towel ring stand is, you can judge for yourself whether the stand should sit on the counter or the floor.
If you have a short towel ring stand, you can place it on the counter. If your towel ring has a stand that stretches over 12”, you should place it on the floor.
Ideally, your towel ring stand should be a few inches from your sink so you can wash your hands and only have a minimal reach to dry them with a towel. The position that gives you and your guests easier access to a hand towel is where you should place your towel ring stand.