Dear me - hundreds of places to go! Judging from your timescale (4 months lef tf rthe whole of the western Med, and that's March to June) then suggest you stay away from the mainland and focus on Sicily
(particularly northern coast, which we haven't done yet), then Cagliari which has some fab museums, sail up either coast of Sardinia - we came down the east coast
and enjoyed Olbia but avoid the Costa Smeralda. The Maddalena islands are fantastic, and then you can visit NW Sardinia. We only went to the Asinara National park, but as Anjou says it's all lovely there. Once west of the Bonifaccio Strait, watch carefully for mistrals.
Then it depends on where next. You either head
up the west coast
, which has lovely sailing and walking but can be challenging in a mistral, and then takes you to southern france
- great anchoring
and fun places. Or go west to the Balearics, on which I can't comment not having sailed there.
If you are in southern Italian mainland then Pompeii is a must but you might want to stop in eg Troopea and take a train as it can be expensive. it'll stay cheaper till end April and then prices climb steeply.
Alternatively then go from north of Naples, across to either Sardinia or (a long trip) to Rome and then the Tuscan Islands (lovely) and across the northern tip of Corsica
. This would give you more Italian mainland, which is great, but longer passages and possibly more expensive places to stay (depending on your timing).
HTH and fair winds.