I make it a point never to use public computers; I travel with a used laptop with a VPN installed.
I came across a good article entitled, "You Should Treat Public Computers Like Public Bathrooms". It shows you what to be mindful of if you have no choice but to use a public computer.
"When I was in college, the main campus library had several computers set up on the first floor for public use, and invariably, whenever I used one, a previous user had not logged out of her Gmail account. So when I tried to load my account, I would instead find myself staring at the entire contents of someone else’s inbox. Of course, I would then log that person out and sign myself in—but those brief moments when I had complete access to another person’s email were terrifying nonetheless. How could people be so careless with something as valuable as their email account?" -Josephine Wolff