Can I play Pokemon Go in a country that I am visiting?

The game field is global. You can play it all over the world. This is both evidential from Ingress and the current Pokemon GO user base who play it globally at the moment with downloaded APKs.

You can only play Pokemon GO if the server allows you to play from the country you are visiting, as evidenced by this incident involving an Australian expat who visited Singapore and wasn't able to play Pokemon GO. They seem to allow/block based on IP address geolocation, since there is an article with instructions to use VPN to workaround the block.

Since there had been reports about people in Europe being able to play the game before the game is officially supported, the server evidently allows many countries beyond countries officially supported.

You can check the list of supported countries on releases.com, or follow the news and social media to see whether the game is supported in a particular country.