In front of the city's harbour is a peninsula which gathers most of its points of interest: Church of Saint Donatus, archaeology museum, roman forum and remains...
If you go down the coastline, you'll find Camping Park Soline**** or Camping Diana and Josip, not far from Biograd na Moru and only 700m from the beach. Once you're there, you can reach the many islands at sea in a short boat trip or canoe ride.
Many water sports are available while you're staying in the area (jet-ski, scuba diving, paddling, canoeing, kayaking) but also laze in the sun and enjoy the gorgeous, large beaches of fine sand. The campsites of Zadar - or closeby - have a water park with pools and slides - surely your kids will love it. Overall, you should know Zadar is one of the tourists' favourite spots in Croatia.