I think having a second gmail address just for emailin yourself files for public computers might work for you. Keep your personal email safe, and forward what you need to the other address. It's a good compromise.

Don't underestimate how vulnerable you are when your email gets hacked - virtually every service you use can be accessed by the forgotten password mechanism when your email is breached. I'm pretty lazy and have procrastinated for a long time, but with the recent attacks and realizing what a mess I could face if hacked I finally implemented two factor auth and I have no regrets yet.