Public restrooms can actually be good places to wash hands, because majority of restrooms have those dry blowers and disposable papers (naturally) - basically, you come into very little contact with potential fomites, if you do it right. I'm of course talking about those better equipped restrooms with a certain level of quality. Those of highest quality even have sensors on their taps, so no physical contact is required. That's a brilliant invention, as taps are more often the not one of the biggest transmitters of infectious particles.
Drying your hands and/or face with a regular towel is not the best thing, though. Having your own personal towel is a good thing, but that thing can carry bad stuff in great amounts, if not regularly washed and cleaned.