Hi, D..
My 11-month-old daughter just got over a stomach bug in which she had diarrhea for over a week. Luckily, we were home and could take her to the doctor, which really didn't make much of a difference because there isn't any medicine you can give and there isn't anything the doctor can do when they do get sick like this (I wasted $35 for each of two visits I made while she was sick to hear what I am going telling you now).
However, what he did recommend was that we made sure she was properly hydrated, preferably with pedialyte or other electrolyte drink, and that she was on a bland diet (i.e. apple sauce, rice cereal, bananas) because that seems to help with the diarrhea. She had a fever for the first three days of it, so he recommended infant Tylenol.
She was playing like normal, so besides the fever and the diarrhea, it didn't appear like she was sick. Just make sure he's hydrated.
If it goes longer than 10 days and he appears to have lost weight, I think that warrants a doctor visit. If you doubt anything I have mentioned hear, you should just give your son's pediatrician a call.
I hope he feels better soon and you enjoy the rest of your trip!
Good luck!
E.