Jay (Eire)
12508
As many others have already said, the answer is destination dependent.
I travel to Japan, HK and Singapore regularly and for these trips I have no concern wearing a nice watch.
In Europe and the US I may or may not adjust wristwear based on specific location, Seiko and Swatch being the ultimate backup should the destination dictate. Sometimes the backup is Rolex.
My primary rule for all travel is only one nice watch, I do try not to leave anything in the hotel safe regardless of country.