The Fabre Museum: Has been going through major construction and refurbishing in the past few years. This is one of the largest museums in France and contains over 800 pieces from Italian, French, Flemish, Spanish and Dutch artists.
Place de la Comedie: the heart of the city and lined with cafes and shopping. This is also home to markets, and you must see the Opera and the Three Graces statue.
Beaches: Montpellier is also famous for its beautiful and pristine seaside. Escape to Montpellier’s beautiful coast and fantastic beaches far from crowds and concrete resorts.
La Promenade Royale du Peyrou: A park and oasis from the bustle of the city. It's also right next to Montpellier's replica of Paris' Arc de Triomphe.
Odysseum: Discover Odysseum, the new area just outside downtown, and its world of leisure and sensations. Odysseum is a unique and innovative complex that combines exciting activities with shopping, offering an extraordinary architectural feast influenced both by Ulysses and Space Odyssey.
Source: http://gofrance.about.com/