A 23rd-century federation president was shown in Star Trek IV: The Voyage Home and Star Trek VI: The Undiscovered Country (played by Kurtwood Smith).
President Jaresh-Inyo, a Grazerite (played by Herschel Sparber), held office in 2372 shown on Star Trek: Deep Space Nine (episode: "Homefront"). He faced an attempted coup led by several Starfleet officers caused by paranoia over Changeling infiltration.
The president's office is in Paris, France, on Earth.