Every island on this list is worth your time. The question is which combination is right for you.
If you want luxury, nightlife, and the most varied experience on a single island, Hvar covers the most ground. Hvar Town for evenings, the interior for mornings, the Pakleni Islands for days on the water. It's the island that works for almost any kind of traveler, which is both its greatest strength and the reason some visitors find it slightly overwhelming in high summer.
If authenticity and genuine escape are what you're after, Vis is the answer. It asks more of you logistically but gives back more in return. Come without a full plan and let the island decide the day. If you need to stop moving and actually rest, Mljet is where that happens. It's a deliberate, unhurried island for people who are ready to let the pace drop and stay dropped.
If culture, gastronomy, and history are your primary interests, Korčula offers all three in a setting that hasn't been overbuilt. It's the island that rewards curiosity: the more you look into it, the more it gives back.
Whichever combination you choose, the Adriatic will be the same: impossibly clear, warm from June through September, and patient with those who take the time to really see it.