Best Italy quick trip from Nice?

San Remo or Ventimiglia is about all you will be able to reach in 4 hours, if that's what you mean by half-day.

https://www.lonelyplanet.com/italy/liguria-piedmont-and-valle-daosta/san-remo

https://www.lonelyplanet.com/italy/ventimiglia

Ventimiglia is about 40 to 50 minutes on the train each way, (sit on the water side, on the right heading to Italy, left on the way back, upstairs is best) so you can have a couple of hours there to wander the town or go down to the water. The regular commuter train from Villefranche sur Mer will take you there.

San Remo is about 90 minutes by train. You have to change to an Italian train in Ventimiglia and often have 20 to 30 minutes there. Some are Italian Regionale trains and your ticket will be valid on any of them. Some from Ventimiglia to San Remo are IC - Intercities - and require a seat reservation. With a normal ticket the IC reservation will be built in but you need to take the train reserved. If you have plans to make the journey using a Eurail pass you need to know that you need a passholder reservation on IC trains in Italy which will cost you upwards of €3 pp per leg.

So with 3 hours on the train to San Remo that doesn't leave you a lot of sightseeing time - either extend the time or plan on a very superficial visit.

Savona gets nice reviews. The historical center was influenced by the Genovese. It’s about 3 hours by train from Nice.

Thank you both!

I would immediately drive to Dolceacqua ---- lovely bridge, medieval core, castle, good food. Google says 1 hour and 1 minute from Villefranche sur Mer. We spent 3 nights there last November.