Brancaster is the best beach - miles and miles of sand when the tide is out and dunes and rocks for the children to climb on. It's completely unsheltered from the wind though - you'll need a wind-break!
Wells-next-the-Sea is also nice - it's more sheltered than Brancaster and there's a long line of beautiful beach huts (which sell for ££££££!). Again, miles and miles of sand when the tide is out.
Swimming pool in Sheringham is good (wave machine is good fun).
Loads of fab pubs for food - we particularly like the George in Cley, the Hero in Burnham Overy Staithe and the Jolly Sailors in Brancaster Staithe (I think - some of the villages along the coast road tend to blur into one!).
Holkham Hall is lovely and the beach is also amazing, but it's quite trek through the pine trees to get to it. Holkham have some good outdoor events during the summer - we went to see Alice through the looking glass one year, and they had great stuff on over Easter. It's worth checking out to see what's on.
Last time we also went to Houghton Hall, which was good - beautiful gardens and we've also been to Sandringham, where the guides give you all sorts of inside info about the Royals 
.
Burnham Overy Staithe is lovely - there's a great harbour for crabbing.
Blakeney is also lovely - good crabbing and a few nice shops to wander round.
Burnham Market is a bit Fulham-on-Sea, but there's some nice shops to poke around in - a lovely deli, really good butchers and bakers. There's also a women's clothes shop called Lime Green which is a bit £££, but upstairs they have second hand children's clothes, which are all Joules and Boden! Got some great bargains when we were there last.
We were up at Easter and go up again for the Jubilee weekend - can't wait (just hope the sun shines for us this time!).