The center of the city...literally!
So I was thiking of a place that you definitely should go if you are in Montpellier...and I realized that there's one place in the city where you can always see people walking (no matter if it's 2am), there's a place where you can find different restaurants and boutiques, there's a place where people can choose on going to the movies or going to the theatre; this place is La Place de la Comédie (or as people call it, Comédie).
This is was the meeting point I always set up with my friends. Whether we were going shopping or eating or drinking, we always met up at Comédie. Also, if you want to go anywhere in centre-ville, Comédie is close enough to walk there. At Comédie you'll find Montpellier's tourism office. Furthermore, Comédie is just a 2 minute walk from the Train Station (La Gare), and Corum, a convention center.
So, if you're thinking of a place that captures Montpellier's soul: its diversity, its culture and its charm; then you should go straight to Comédie.