Stops along the train route from Antibes to Rome

I presume you will be traveling along the Italian coast, although some faster trains might be through Milan. You will change trains in Nice (Nice Ville station), then probably in Ventimiglia on the Italian side (and then again probably in Genoa and La Spezia).
Along the Italia riviera there are numerous towns you might like, like Camogli, Sestri Levante, Moneglia, Monterosso (or any of the Cinque Terre towns).
Between La Spezia and Rome along the Coast there isn’t much to be worth a stop. I like Castiglioncello near Livorno but anything else is so so. Southern Tuscany would be nice but nice towns are not really along the railway so you’d need a car. Grosseto is a small walled city (like Lucca) that is worth a visit.
On the French side I like Menton too, right at the border with Italy.

The Italian Riviera is lovely. The Cinque Terre is amazing but also mobbed with tourists much of the season. Camogli to the north is much calmer outside of summer - a really lovely little seaside town.

I only saw Antibes on a day trip, so I can’t comment on staying there, but have stayed in Menton twice and obviously like it a lot. French with an Italian flavor. I also liked Ventimiglia, and Bordighera, although again I only saw them on day trips.

I think Antibes would be a wonderful place to stay for several days. It has charm, history, a Picasso museum and is on the water. Perfect!

Hello zagfam, here are some suggestions with the caveat that I have not been to all of these places (or it was long ago) but here are a list of suggestions based on a mix of personal and other people's reports.

Antibes is lovely, elegantly French and would make a wonderful stop. You could do Cannes as a day trip and the same with Nice. Nice is a large city that some people love and others tolerate. Old Town Nice - especially on market day - is really worth experiencing.
Nearby Toulon is a larger city, feels blue collar and "resorty" but way less upscale than other French beachside towns. Nearby Hyères is smaller and more charming and has more of that "French Med" experience.

I'd pass on Monaco - maybe an afternoon stop on the train if you're curious.

Onto Italy - since this is the Italy board - everyone on here will recommend Cinque Terre but there are also towns around there that are interesting and much less touristy.
Skipping Portofino - next are Rapallo and Santa Margherita Ligure - are less fancy but are still very upscale. Depending on when how late you're going they may be less crowded and a little quieter.
But past those towns are Chiavari and especially Sestri Levante (7 minutes apart by train) if you want to experience smaller Ligurian cities on the coast just living the Italian Med lifestyle everyday.
Passing over CT you could also look at the southern side of the La Spezia bay.
La Spezia itself is very work-a-day Italy but that's where the train stops but you can easily bus to Lerici - the biggest town on the coast with a charming seaside walk and marina. North of there - connected by seaside sidewalk - is San Terenzo a smaller seaside town and to the South is Tellaro which is what a CT town looked like before tourism. Lerici especially has a summer holiday feel but the tourism is mostly Italian so it doesn't feel the same as hearing everyone speaking English - at least to me. The coastline connecting these areas is beautiful and just over the hill is Sarzana with the small Italian town feel and a bunch of restaurants.

After Liguria I have less experience to offer on Tuscan coastal towns except that many of them are new and focused on seaside escapes for the people from Lucca and Pisa etc. Livirono is a big city and has a reputation for being unusual for an Italian city as a melting pot of different immigrant cultures over the centuries and Venice like canals in the old city. It's on my list to check out in the future but if it sounds intriguing you might check it out.

Sounds fantastic, have a great trip,
=Tod