Budget friendly, not as far from east coast, non-stop flights, five hour time change instead of six points to Portugal.
We also loved our time in Galicia and the Basque country of Spain.

Thank you all for the responses! Yes palenq we have seen some of Italy (Venice Florence Bologna Siena), Spain (Madrid Córdoba Granada Segovia Seville) and Ireland. I appreciate all of the suggestions.

With only 10 days, I wouldn’t go to Croatia – not enough time on the ground.

Depending on what you want to see and do (and with only 10 days) either Northern Spain or Portugal could, IMO, be a great option.

Côte d'Azur is all what you're looking for, except for the high heat !
The TER (Train Express Régional = local train) frequently shuttles between Cannes and Menton with stops at Antibes, Nice, Villefranche-sur-Mer, Monaco... in downtown !
Direct Fly from NYC to Nice a plus ;-)