I heartily second Google Fi. It has worked flawlessly for me on trips all over Europe, India, central America. It's of course always going to be pricier than getting a local SIM, but you can't beat the convenience of having things "just work" from the moment your airplane touches down, and not having to worry about getting a local SIM.

Alternatively I've heard T-Mobile has some good plans for international travel that let you do the same - use your US number seamlessly all over Europe.