What's your favorite Greek island?

I've been thinking about planning a trip to Greece and was wondering, what's your favorite Greek island and why? There are so many to choose from, and I feel like some of the lesser-known ones might be hidden gems.  

Santorini, Mykonos, and a few others always get hyped up, but from what I've heard, they can be overpriced, overcrowded, and not necessarily the best representation of what makes the Greek islands so special. Sure, the views in Santorini are iconic, but is it really worth the insane crowds and expensive everything?  

So, I'd love to hear from people who have explored beyond the usual tourist spots. Which islands have the best vibe, the best beaches, or just feel the most authentic? Looking for any recommendations, big or small islands, lively or quiet.