Enough to do and see for three days? And maybe do an easy daytrip?
You'd have to answer the "enough to do" question yourself based on your interests,reading and research. Montpellier is a gracious university town with a large student population which makes it pretty noisy at times, especially hot summer nights when there's no AC. The Musee Fabre has an excellent small collection including the locals Bazille and Fabre.
Montpellier has many new modern architectural gems. I went to see primarily this because of a similar Bofill construction here in Paris, but it's not everyone's thing and you might not be interested.
https://en.wikipedia.org/wiki/Antigone,_Montpellier
If these aspects are of little interest the lively working fishing port of Sete is fascinating when the catch comes in. There are numerous good seafood restaurants.
I have flown in and out of Montpellier- smallish easy airport, but have only been in the city for a couple of visits and lunch. However, it is within day trip distance of my favorite part of France: l'Herault where there is a wealth of sightseeing opportunities, including the Gorge d'Herault and Pezenas. It is also close to the Pont du Gard, and Sete is a wonderful town to visit and have lunch. Other day trips are Arles and the Camargue, the estuary of the Rhone River. Google Herault and you will find some tourist information. You can easily fill 3 days in the area.
Go for it. There's an atmospheric historic district and plenty of day-trip possibilities.
I spent a month there - December 15 to January 15 - considering moving to France.
Rented an airbnb for the month, which worked very well.
Lots to do there and various short train/bus rides to cities on the Med. Public transit is very good and reasonable; get the 10 trip card.
Recommend the Garden of Plants (interesting story), zoo (nice and free), Place de Comedie (center of town), and just wandering around; old part of town is fun. The city is very walkable and google maps on your phone works pretty good, unlike some places in Spain.
Shopping center at the end of tram #4 has an ice skating rink, climbing wall and aquarium. Day trips to various nearby towns are easy and cheap. Cafe Gazette always has something going on - usually music in the evening - and mostly free. Several pretty good tennis clubs - all clay courts.
The Internations chapter is pretty active and there are a fair number of activities on meetup.
I lived there for a year and never was bored.
Thank you all for the positive feedback
The whole area around Montpellier is a hidden gem of France. We spent 5 weeks there and didn't run out of things to do and see.