Food - local sea food, fish, swiss chard, olive oil, soparnik, rozata (the last 2 i can't translate in english but people will understand you)
Places to stay - Vis, Brac, Split!, every island, avoid Dubrovnik - overrated and tooooo expensive
Hiking - not my thing, but please if you do go be equiped as you should and never go if it's too hot (temperatures rise up to 45 degrees)