I can pass on some observations about interpreting life, based on the experiences of friends and colleagues:
It is perfecly possible that you might be an interpreter and not travel. This would mean interpreting for groups and visitors to your country. One of my friends used to interpret for UN projects, but never left Indonesia.
As far as travelling goes, I understand that you're basically "assigned". The school I used to work for also sourced interpreters for a local auto parts company, and that meant the interpreters being sent to overseas factories for a couple of weeks, along with the bosses, specialists, engineers etc to work during factory tours, meetings and presentations. I was told it was a case of long days talking non-stop in two languages, and perhaps the topic wasn't so interesting at times! I guess at the end of a long day, you'll just want to sit in your room and say nothing. :)
Any other background such as business, engineering, medicine and so on might also influence the kind of work you'd get. Unlike translation, where you can work quietly and research anything you're not sure about, as an interpreter you have to produice the results immediately.
In the end, I think it's still possible to travel with some freedom and still work as an interpreter, so perhaps other italki members have a more direct experience of this.