I was in Rome in March a couple of years ago and loved it. If you can get out of the city, go to Tivoli and see the Villa d'Este. A must see if you are interested in landscape history.

On lake Maggiore near Como is Isola Bella - a great garden, but haven't been in March/April so don't know the weather.

In France, go see Villa Ephrussi de Rothschild in St. Jean-Cap Ferrat, just east of Nice. A really nice garden, surrounded by the Med. Nice has lots of good gardens as does Monaco. There is a nice garden just outside the Palace in Monaco. Nice has a botanical garden that focuses on Med. plants and tropicals.

In case you haven't left the states yet....

The Cinque Terre, Italian coast east and south of Genoa (Genova) is spectacular (at least in October). Small towns perched on the craggy coast, perfect for walking and biking or you can take the commuter train link or little green buses from place to place. Great seafood and matching white wines......

Genoa also has several gardens listed as topnotch. Villa Durazzo Pallavicini, Parc Villa Grimaldi, and Villa Negrotto Cambiaso Pallavicino are all nearby and open daily.