I'd recommend finding a nice cafe in Place de la Comedie, take a good book, get yourself some coffee and sit and people watch, or building watch (they're beautiful). Place de la Comedie is a big pedestrian bit in the middle Montpellier where there's often stuff going on like street entertainers. I could sit there in an outside cafe for hours.
There seems to be a lot of students in Montpellier so there's quite a bit going on in terms of nightlife too if you're feeling brave.
There are also galleries and museums that I don't know anything about although there's one in an old church that's supposed to be good. I don't know the name (Anne something), I'm sure you could google it.
Well I'm here. City is pretty, people are nice (really) and the streets are insane (can't find my way around).
How did I get this gig? Work related, my company is a IBM Business partner and IBM Montpellier Performance Center is evaluating the Oracle Add-in for RPT we created. I got sent because I'm technical and my Passport was up to date.