@julian-wolf sorry for the very late reply. I don't connect much to the internet lately. I must say the other members have already given good advice (particularly that of Cucoo imo). I can't tell you much about Liguria cause I was there a long time ago. if you have some time to visit Umbria is another beautiful region in the italian hinterland where you get amazing food and a lot of small medieval villages which are usually not overrun by tourists, unlike for example Tuscany or Lazio. Basically every single region in Italy offers his typical kind of foods which are different from the other regions and man it would be worth try them all. prepare to put on some weight. Venice, Milan, Turin, Florence, Rome, Naples, Palermo are just a few cities to mention which are all worth spending a few days in. but there are many others, the town I live in (Verona) for example is a small and nice city constantly packed with tourists. history is everywhere. Greeks, romans, middle ages and so on.
The southern regions have a warmer climate and in April you can already find summer temperatures. In Sicily i absolutely recommend you visit Palermo and its markets where you can find all the local products. All of Puglia is beautiful, land and people. I didn't give you detailed informations, I know, but trust me, wherever you go you will find something interesting to visit and, hopefully, good people. I hope you will have a good time here and if you need any further information don't hesitate to write to me here, I will check more often now. cheers!
Ale
