Are you sure the drop off fee is that high? I never had to pay in the past, and this year for the first time Im told I’ll have to pay a drop off fee of €15 (not really that huge). I used www.AutoEurope.com, like every year.
Regarding your travel plans. I don’t really care for Olbia much. I’ve used it only for flights at least 4 times, but I wouldn’t care to use it as a base for anything. Since you have a car you can certainly find better places in Northern Sardinia. I generally stayed in the Santa Teresa area, but there are many places in northern Sardinia that I would use before choosing Olbia.
I have never been in Southern Sardinia, so I can’t speak about Cagliari, however I bet I would feel the same about Cagliari. Aside from a Castle (Bastion of St. Remy) and the cathedral, both in the Castello district, I don’t even know what else Cagliari is famous for.
In your shoes, if you are flying to Olbia and only have a week, I would explore the north side of the island only (the better half of the island). As I said the Santa Teresa area is good. I love Santa Teresa. From the harbor definitely take a boat excursion to the Maddalena Archipelago. You can also visit Bonifacio in southern Corsica, The ferry from Santa Teresa takes 45-50 min, and you don’t need to take the car across if you don’t plan to explore Corsica, Bonifacio itself is an ancient town that is best done on foot. Other places that are worth visiting is Capo Testa (Cala Luna is a great beach, no need for bathing suit either, clothing is optional), Castelsardo (one of the quaintest towns in Sardinia just an hour drive from Santa Teresa), Stintino (2 hr drive), Costa Smeralda towns like Porto Cervo or Porto Rotondo. Expensive places for the rich and famous VIPs (like Berlusconi, Aga Khan) with huge yachts and villas, but you can visit as a day trip since it’s only one hour away from Santa Teresa.
I gave more suggestions in the past, see below.
https://community.ricksteves.com/travel-forum/italy/sardinia-a4b6bf34-12f0-4f41-aa46-cc7c08ab1f7f
One year (more than 15 years ago) I stayed in the place below at Capo Testa. Lots of fun but not fancy. I cheap. If you have a car (the place is just outside town in Santa Teresa) it works. But there are lots of choices all over.
https://www.hotelmiragesardegna.it/en/