A fussy way of writing the sentence is "To which countries have you been?" That's if prepositions at the end of a sentence REALLY bother you. Still, putting "to" at the end is fine because you've already given what "to" is normally placed before: which countries. If the information is already there, then why repeat it? :) If you cut out the "to", then you have a real problem. "Which countries have you been?" means I have a history of existing as a number of countries. "In my employment history, I have been a waiter, an accountant, and the Republic of Macedonia."

Because prepositions always go to the end of a sentence!