There are number of great hiking trails without much crowds as most people only resent to most visited sections of island, anyways. Those are beautiful too, of course and can lead you to some of most spectacular view points or landscapes, especailly when you're searching for views over cliffs. Well, most of other are pleasantly lonely, here or there a hiker, a bird or insect, or snake interrupt silence.
Far best idea for those who'd love to learn more about paths and topography is to buy the map, the largest one for that purpose can be bought at the tourist office in Sali and cost 10 Kuna. Other then that, the trails are well marked, so just follow the red signs for directions you'd like to go. Terrain can be rough to mild or flat, and good boots will add to safety where talking of rocks. Whenhiking you can get pretty far from settlements so bring enough water, food and sun protection (and wind too if you're not there in summer), cover your head, bring swimming gear and whatsoever... you shall know when you're choosing trails.
Beside swimming, walking will be one of best things to do on island.
On photo below there's main path between parking place towards salty lake Mir, the one that is actually easy to do and will take about 2 kilometer distance.
With rich aquatic ecosystems and crystal clean sea, Dugi otok is in my opinion one of best places in Adriatic, if not in Mediterranean regions altogether for snorkelling. I am not diver myself, but I suspect it's great too. Surrounding seas are full of interesting wildlife and stunning submerged landscapes covered with lush vegetation. You can spend hours in water swimming in group of tiny fishes and if real lucky, maybe you'll spot dolphin. In many places sea bed falls steep into depth where different light appear - and sometimes, just few meters from rocky shore, it becomes 40, 60 meters deep!
For swimming there're great spots too, and it only depends what type of coast you like:
you've got rocks which are predominant of Dugi otok and at most length due terrain. Good spot with rocks to swim and snorkel are around Božava, also Sali and in gulfs and coves of Telašćica. You've got pebble beaches which are by Lopata - Sakarun, Veli Žal and patches of it at Veli Rat, also at Brbiščica.
Sand there is too - and it's in Sakarun.
There's also swimming in the lake Mir with donkeys on the beach and healing silt on the bottom, it0s crowded place. Where tour boats unload tourists in a gulf near the lake, there is another beach, half concrete and crowded that it's best to avoid as there are so many nicer places around island.
And there are more places I cannot mention because it would take several weeks to walk the entire coastline... but basically, where there're settlements its never to far to any decent swimming spots.
Equipment: Take snorkel mask and jump straight into water.
We didn't see many sea urchins here.