Ventimiglia is accessible by train, it's the first town in Italy if you want some change of scenery. It's not that much different, but hey it's another country. Genova is a bit too far.
For a day trip I would advise to try and visit the Lérins islands near Cannes. They're pretty comfy, with a monastery on the bigger one. Beware their merchandise is overpriced. You can get the ferry from Cannes, you'll get on the islands within 10-15 minutes.
Cannes itself is meh, you can try walking on the Croisette if you like. Some might find it pretty, but it's pretty average compared to any other coastal town in the area.
If you want to do some bathing, I wrote some detailed posts on previous thread and cba to type it again tbqh, but basically the best beaches are la Mala in Cap d'Ail (quite small though), Villefranche-sur-Mer (plus you can visit the small town), Beaulieu-sur-Mer, le Larvotto in Monaco, or Antibes if you prefer sand. Eze might be good but I don't know it well, though the village itself is nice to visit.
Picrel: OC of the Mercantour.