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Sicilian here.
Etna volcano is surely one of that places, great nature and panorama, great for camping with tent.
Obviously there are beaches everywhere, if you have a boat/yacht and you search for a touristic harbor you could visit my hometown Riposto (near Catania and Taormina), it's also a good place to reach because it's located in the only part of Sicily with double railroad and near the Catania Airport.
If you are interested in Greek art there are Agrigento, Taormina and Siracusa,
But be aware, Agrigento have wonderful temples but it's arid as a desert and have a poor organization, Taormina is glamourous and quite easy to reach but it's fucking expensive.
Most major cities have lot of history and art but are chaotic, dirty and in some places dangerous (like most of Italian big cities),
there's more to say but it's better you read something like lonelyplanet guides..
also: some people doesn't speak English, but younger educated ones should know it well. In the Etna's territory German is a must-known in a lot restaurant and hotels, and where I live the train ticket are printed in Italian and German, so if you speak it is a plus...
Like in any other places you can find good people and morons, just avoid dangerous ghettos and I can assure you that visited as a tourist is better and safer than MOST parts of Italy..