The Palais du Luxembourg has a storied history as the early 16th-century home of Maria de Medici, the Italian wife of French King Henry IV. Today, it is home to the French Senate; the Palace is open for group tours when the Sentate is not in session.
Also included on the grounds, and until recently under the supervision of the Senate, is the Musée du Luxembourg, France's first public museum. The works originally shown there have since been moved to the Louvre, and today it shows important exhibitions by classic and contemporary artists. It has a constantly changing exhibition schedule, so even repeat visitors can see something new.
The closest public transportation route is via the RER C line; the Luxembourg stop brings you into the grounds of the Jardins du Luxembourg.