It really depends on what your are looking for in a restaurant, but I would recommend the following:
Finz is on waterfront in Salem. Nice place, good food. You can walk around & see the sights as well.
http://www.hipfinz.com/ Cygnet is in Village of Beverly Farms, down the street from Prides Crossing, and a few miles south of Manchester-By-The-Sea. Very nice, great food, and quiet ambiance.
http://cygnetrestaurant.com/about-us/ Alchemy is nice & cozy, as is its sister restaurant, Latitude 43 in Gloucester, but food is average. It is owned by the same people that own:
Hale St. Tavern, Beverly Farms
15 Walnut St., Hamilton
Cala's, Manchester(BTS)
Maggie's Farm, Middleton
Minglewood Tavern, Gloucester
(All decent places, with good beer selections, but food is decent but not outstanding.)
Have fun discovering the North Shore. Its a great place.