You can hang over the cabinet door towel racks. Buy one for bath towel and the other the other bath towel (don't most girls with long hair use 2 towels?) or face towel. Good for thin closet doors.
Amazon.com: 14" Bath Towel Bar - Over-the-Cabinet-Door (Brushed Stainless Steel) (2.75" H x 14.25" W x 2.25" D): Kitchen & Dining