If you mean by underrated "drop dead gorgeous yet ignored by most international tourists" then I'd say Karpathos, Serifos, Astypalaia and Kastellorizo. I have a soft spot for Chios too. I just came back to Athens after visiting Astypalaia and Kastellorizo among others and loved the experience. They should fit your description - although each island has its own unique strong points and weaker points depending on which aspect is more important to you.

There are probably many more but I've only visited 15 islanda so far so can't comment more! Especially the Ionian islands I never really visited besides Zakynthos.

I like Naxos too (it was also part of my trip the past weeks) and this year is a great chance to visit it. Compared to other times it is pleasantly empty, although in the evening hours there is life in the taverns of Chora Naxos. The great aspect of Naxos is of course its size and mountainous interior - there is a lot to see and its great for hiking.