It’s really your preference; there is no set height.
Ultimately it is up to you and your preference. If you are shorter you may want it a tad lower, if you are taller you may want it a tad higher. But generally towel bars/rings are hung at about 48 inches from the floor.
~Your All-Star Team
The National Kitchen and Bath Association recommends towel bars hung between 30 and 48 inches off the floor. If only one towel bar is used and is in line with a vanity, for instance, aligning it at the same height as the vanity is one option.