Mjlet is an island 1 1/2 hours from Dubrovnik by ferry. The majority of the island is uninhabited, and it hosts a large national park.
I recommend it for 1) Its walking trails. You could walk for days and never take the same trail twice, and 2) Its beauty. The blues and greens of the trees, sky, and water are more vibrant than you'll find elsewhere.
Trip report and photos: shallowmusings.typepad.com/travel_musings/
Here's the national park website:
www.np-mljet.hr/
Arrive at Graz Harbor around 7:15 am to catch a ferry. The ferry is less than $20, entrance into the park is $20. Debark at the second port. Buy a map or you'll get lost. There's a hotel on the island (accessible from the port by bus) but I didn't stay there (and I regret it). The Mali Raj food was overpriced and underquality: hold out for the restaurant at the monastary.