where are they

Well, the FBI is certainly in Europe and many other countries. The show does exaggerate their role; generally they coordinate with local authorities and largely don't strike out on their own. For drama's sake, the show has these agents involved in more countries than they would likely to be in. (Most countries have their own FBI legate offices attaches to the US embassies) Obviously to avoid having a different cast each week, or be forced to set stories in only one country, this team travels more than it should.

I've never seen this show, but the premise is absolutely ludicrous:

"The series follows members of the FBI's international "Fly Team", elite Special Agents headquartered in Budapest who locate and neutralize threats against American interests around the world principally in Europe."

I mean, in their dreams!🤣 What toddler came up with this show???