NOT a Sardina expert - but we spent a couple of weeks in Sardinia in April/May 2018. The weather was largely good - a couple of rainy days though. It was not warm enough to spend time on the beaches sunbathing and swimming though. If that is the experience you want, I would go later in the season. If so, consider staying near Olbia and enjoy the emerald coast beaches. We rented an AirBnB in Alghero on the Northwest coast. Alghero is an old port city with a historic center that has a lot of Catalan influence due to its easy sea access to the Northeast coast of Spain. There is no single place to stay that is "super-convenient" to everywhere. Alghero as a base though worked for us.
We took the overnight ferry from Civitavecchia to Olbia and rented a car in Olbia and drove to A;ghero. A car is essential in Sardinia. The ferry was clean and comfortable, but really most of our time was spent sleeping. If I recall correctly, it was about a 10 or 11 hour crossing. There are flights to both Calgiari (southern tip) and Olbia. We flew out from Calgiari to Marseilles and spent a night in Cagliari - a large port with a hustling and bustling port area. A wholly different experience than sleepier Alghero. If you are planning to go to Corsica afterwards, I understand there is a ferry from Porto Torres to Corsica.
There are interesting ancient stone structure called nuraghi scattered throughout the island and are remnants of the Nuraghic civilization. Each is different, some large, some smaller. Depending on where you are staying you can figure out which would be most convenient to see,
Le Prigionette Park had gorgeous sea views from rocky cliffs. It is not to far from Grotto Nettuno, which we also visited.
There is a preserved Phoenecian-Roman port called Tharros near the town of Cabras that was interestting.
If you can get to the Girara di Gesturi you can see some of the last remaining wild horses in all of Europe. We there for the ranunculus bloom so it was an especially beautiful sight.
We also visited Su Gologone, a huge natural spring in the center of Sardinia. We had a great lunch at hotel there that was a facility worth seeing (or staying at if it is your budget). It is a favorite of various celebrities low-keying it in Sardinia (e.g., Madonna, Brad Pitt, etc.). Each room is unique with amazing artwork and the common areas and setting is exquisite.
https://www.sugologone.it/en/
Millenary Olive Trees - Sardinia's claim to Europe's oldest olive trees - 3,000 years or so old.
Lot's of sheep in Sardinia and pecorino cheese abounds.
That's what is in my memory at the moment. Would have to go back to my journal and pictures to get more detail. Have fun planning.