Three nights - Caceres or Merida, or both?

I day-tripped from Caceres to Merida by train back in 2016; that was plenty of time for me. I even had time to traipse over to the (underwhelming) sculpture park and have a sit-down lunch. Merida didn't seem to have a very expansive historic district.

However, I'm not the best person to give advice on how much time you might want in Merida, because I'm really not much interested in ancient ruins. Would Googling for photos help? I did enjoy the mosaics in the nice archaeological museum, but ruins and museum aside, Merida is not a very interesting place, I don't think.

Mérida is not very interesting besides the ruins and the museum... But those are among the best in the Roman world. I still prefer Cáceres and Trujillo to Mérida.

The ruins are extraordinary--if you are passing by, I absolutely would not miss them. They are certainly in the top five/six of ruins I have seen (Pompeii, Istanbul, Athens/Peloponnese). The town was pleasant if not particularly exciting, but certainly not dismal--families everywhere, shops and restaurants, friendly people (I recall a parking attendant going the extra mile to assist us). I'd compare the time to day trip versus the time to spend an overnight. I wonder if you could even do a stop over if schedules work out? But I don't think you would be bored if you stayed the night. We drove from Caceres to Merida, had lunch and then spent the day exploring the ruins. We regretfully skipped the museum because we were being extra cautious (had to test to return home). There were some things we missed like the riverside fortress. Something had to go, so we skipped Trujillo on that trip.
This is a good overview: https://www.planetware.com/tourist-attractions-/merida-e-extr-mer.htm
In Caceres, don't miss El Figón de Eustaquio, I am hungry now...

Mérida is a hour from Cáceres so it should be an easy day trip. I liked the ruins there. Trujillo is ok and a half day there would be plenty. If your itinerary takes you through Mérida on the way to Sevilla, then spending a night there makes sense. I wouldn’t do it as a day trip, then have to go back through it a couple days later.

Actually I liked Merida (which I visited in 2014) better than a couple of the commenters above, and the Roman ruins were abundant. Two in particular, the Theatre and the Stadium (amphitheatre), should be "big enough" to impress people who have seen Roman ruins elsewhere. The historic center was nice, too, though maybe not exceptional by Spanish standards. I think Merida would be a good choice. However, I also visited Caceres and Trujillo (though back in 2006), and given my interests, which focus on intriguing old medieval cities that still get relatively few tourists (at least for Spain), I think I would recommend spending three available nights between those two cities, at least to those with interests like mine.