Two Weeks in Italy - On our way to Valencia-Spain

Lucky you! Florence may be a little of of your way, but you can't beat it for art. Most people say Genoa is more of a port town, not much else. I have only been to the airport there. I believe a lot of Cinque Terre is closed now, too. Lucca is in between CT and Florence, a great smaller medieval town.

Can't answer about France, haven't been there, yet!

Monaco and the French Riviera are really nice. You can stay in a smaller village such as Eze or opt for a larger city like Nice. Either way, you should have easy access to neighboring towns via train, so you may not necessarily need or want a car. If you want to venture off the beaten path there, keep the car! I would also check into flights to Valencia from Nice. I usually use skyscanner.net for airfares but you can also check easyjet.com, ryanair.com and vueling.com.

Just keep in mind that renting a car in one country and dropping it off in another country can result in some large fees. If you rent a car, I might keep it within a specific country and use the train to cross the borders.

I'd stick to the trains. It's a very long drive with high toll charges and high fuel costs.
Avoiding big city Barcelona, you could do something like ...
Verona >> Milano >> Genova >> Antibes >> Arles >> Girona >> Tarragona >> Valencia

Thanks to all of you who have weighed-in on this. Unexpectedly, we have found that Verona has exceeded our original expectations, so we are still here and will probably remain through the weekend. We'd like to take some day trips around Verona, probably by train although we haven't ruled out the rental car yet, so any suggestions?

We really love architecture and art and have a fascination for the architecture styles of old churches and cathedrals. Verona has really delivered with a variety of styles within easy walking.

Thanks!

Jim