Post-docs are short-term (2-3 year, typically) research positions. One typically has to do a few postdocs before landing a tenure-track faculty positions. Because postdoc positions are short-term and people intent on becoming a professor usually end up doing more than one, they end up moving around a bit (people usually don't do multiple postdocs at the same place). So, this sort of 'travelling' is really just moving from job to job. Postdocs typically go to conferences, too, but it depends on funding.
On the non-academic side, consulting positions typically require a lot of travel, and often hire Ph.Ds. I went to a talk by a guy from McKinsey and if I recall correctly he said he was traveling 4 days a week (he also said not many people stick with the job more than a few years because it's hard to settle down doing that much travelling).
Other companies in industry or finance sometimes also have global offices that you could possibly get sent to.