I live in Norfolk. The Broads are great, you can hire a boat for the week, (depending on childs ages etc.)
Gt Yarmouth is a little tacky, but is ok for a day visit. They have a Pleasure beach with rides etc for the kids, and a pier, also pony rides and a horse and carriage to hire along the sea front. There is also a sealife centre there and I think a butterfly farm. They also do a trip by boat to see the wind farms (the so called ugly windmills which help to generate power)
Blakeney point is also a lovely place to visit, also boat trips to see 'the seals'
Sheringham is a lovely quiet place to visit, very clean, nice places to eat. But small.
Cromer is also very nice, quiet, a pier, fresh crabs and fish, a few shops, nice beach.
Norwich (25-30miles from Gt Yarmouth) has some great shops, a mall, great pubs for meals and some great hotels.