You can take a base any where in the world you like. You do not need the right to work in a specified country. Harder to pull it off with a family but as a single American, you would just have to leave the area before your tourist visa expired (30, 60, 90 days, etc). You do that every time you go to work....would just have to get a stamp on the way in and out. Temp bases are alot easier to pull off.

Example of a domestic ZED....ORD-LGA 33USD one way.

FO