You definitely want to stay in a foreign country for a while if you have the chance to do so. I vividly remember remember after the 9 weeks in Israel, which was my first real leaving of Germany, you come back and realize that you've changed. For the better. You acquire "worldsmanship", and that will stay with your for the rest of your life.
This, most importantly. You learn so, so much about yourself, world, and humanity by living (note, not visiting) with other people and cultures. This is especially important for Americans, who I feel have such a shortsighted and ignorant understanding of the world. I stayed in France a few years back during a summer during a college program and quickly realized how different Americans were not just from the French, but all others. It was an international program and the Argentinians, Brazilians, Egyptians, and Chinese all put my fellow American students to shame in almost every regard except wealth.
Anyway; I fell in love with the city I was in (Lyon) and went back for 10 months two years ago. This summer I am moving there for good.
Do it man; I am sure it will be as rewarding and intellectually pleasing as I am sure your PhD was. I can definitely vouch for Europe, English & French Caribbean, and Argentina; can't say for other countries though.