For a good family day with out the pooch you could always go to Blakeney and go seal watching. then have a nice crab salad/sandwich after I always do that.
Sheringham Park is a fab day out for all too... Dinosaur adventure is awesome... Holkham Hall has a great adventure playground for the kids and loads to do on general
Mundesley beach is lovely, if your kids are young when the tide goes out there are little pools left which is great and safe for them to play in, lovely cafe just above the prom (but only takes cash!)