Tini Martini Bar Saint Augustine, Fl. The Tini Martini Bar is located at 24 Avenida Menendez Street, Saint Augustine, Florida. It is in the Historic Downtown District at the Casablanca Inn. It features music and speciality drinks. There is patio seating overlooking Mantanzas Bay. There is also indoor seating at tables and the bar. The Tini Martini Bar is known for its specialty martinis. It offers hard liquors, wines, and several malt Scotch choices. It also features 20 types of beer.