Bill Clinton could run for Mayor (if he moved to New York City), Governor of New York or even Senator. But it's uncommon for a former President to do so. Andrew Johnson became Senator after his Presidential term was completed way back in the 1870s. William Howard Taft was named Chief Justice of the Supreme Court by Warren Harding in the 1910s. I can't think of any other former President who became a major elected or appointed official off the top of my head.
I would posit that Slick Willie could run for Secretary General of the UN and win. The F-ing French alone would bribe enough third world votes to get slick elected. Why?
Because it would piss off the American Republican Party no end.