Which neighborhoods are safe for a single senior lady in Montpellier?

Here are 3 in my personal-choice order: Hotel du Palais, Hotel du Midi, citadines AppartHotel. Always ask for a courtyard side room to avoid street noise. If none of these work, come back and I’ll check for others.

You don’t need Uber because most of the city center is reachable on foot or by tram. I use taxis first because they are less expensive for the same route, or I use Bolt. Hotel du Palais and Hotel du MIDI are in a pedestrian zone. I’m not sure how close a taxi can get. Do you have mobility problems, or would you be able to roll a suitcase 2-3 blocks?

Thank you! Do you mean Citadines Antigone Montpellier?

Yes. We stayed there for two weeks. It has a tram stop at the front door and a covered market across the street, 10 minute walk to the Place de la Comédie.
The Palais is older, quaint but in a wonderful location.
The Midi is right off the central square, Place de la Comédie.

Which of these were the quietest?

There is no way to predict which hotel will have the fewest people arriving back late or talking in the hallways. But, Hotel du Midi and Hotel du Palais are in very active street-life areas. You could have more late diners returning and making noise. The Citadines is in a residential/office/small business area near the center of town. No matter where, ask for a court side room. The Citadines has a tram stop outside the front door and a garden with tables and chairs in the back.

You asked about areas: I wouldn’t stay near the train station.