March 2018 Best destination for weather in March

Spain. Actually part of it called Canary Islands.

Andalusia
Mallorca
Amalfi Coast
Malta

RS has tours to Italy, Greece and Spain that all begin between March 9 and March 18. I noted those dates because you said mid-March. To get a complete list, click on "Our Tours", then use the "Search" link, and you'll get to an option to see tours by date, choose March.

Spain - Barcelona, Madrid, Andalucia. There's a wonderful festival in Valencia in mid-March. Semana Santa is the last week in March.
Italy - anywhere except the Dolomites.
Greece

Andalucia is the warmest, driest part of Europe.

Also South of Rome. The coasts won't be beach weather but the further south you go, the nicer the weather is likely to be.

The weather can still be very variable in March - in many places, the weather this year was cooler and wetter than 2016. I spent March this year on the Algarve in Portugal, which was very mixed. There were a few beach days, but some rain too. The more south west you are in Europe, the better the chance of decent weather.

Nowhere in mainland Europe is going to have "guaranteed" good weather in March, so do what I am doing in 2018 and head for the Canary Islands, where the weather will be much warmer (almost guaranteed!).

It isn't a good time to go to Greece - most flights there from other parts of Europe don't start until early May for a reason - resorts aren't open and the weather is poor.

Madeira--TAP, the airline of Portugal now has flights from JFK.

Or still in the EU and part of France, the Caribbean Islands of Guadeloupe or Martinique!