A wooden flea-market cupboard makes a great towel cabinet, left. Use top of cabinet for extra storage. Keep your regular supply in the glass-fronted cabinet. Having all towels visible makes it easy to keep track of your inventory. Open shelves on the sides hold glass jars full of cotton balls and soaps.
Towel Cabinet
Organizing Good Things 2004

We put one over a tub area that we barely used, that way it didn't have to be as high,(we have a seperate tub and shower)
BEDA,
I am even shorter than you, and also have a small bathroom. I found that the over-the-toilet shelving units that are sold at bed and bath stores are useful. Especially in the guest bath - my guests are always tall and can reach the top one!
This would not work well in my bathroom as I am only 5'2'. I would need a stool and a place to put it. My bathroom is small.