Traveling Over-seas With an iPhone

This summer, I'll be taking a ten-day trip to Europe (I'm American); spending three days each in London, Paris, and Rome. It'll be my first time across the pond, but unfortunately... it appears that I won't be able to share it with everyone very easily.

I have an iPhone 5 on Verizon, and I've been told by a Verizon-store dude that my only options for using it over there would be to either upgrade to an international plan, or cancel my service here while I'm gone and spend a lot of time public Wi-Fi hunting while I'm there.

I'd like to hear from anyone who, like me, doesn't travel consistently enough to need an international plan, has taken trips overseas, and if/how they managed to use data there.

Or, or worst-case scenario, I guess I'd also like to hear from anyone who lives in those cities that could tell me how feasible running only on Wi-Fi would be. Because I know from experience that even doing so with an iPod Touch in New York was basically impossible.