Lots of people think Sheringham's got a stony beach full of pebbles, but just wait till the tide goes out. It's got a long flat sandy beach which is just great for the kids to play on. The beach is brilliant for building sand castles, but with such a shallow gradient and no sudden drops the kids will be able to paddle all day long.
The town has everything you need for your day trip out, while still retaining its old world charm.
If you're looking for somewhere to stay, we'd recommend www.bookcottages.com/north-norfolk-its-coast.htm , the whole of the North Norfolk coast has so many interesting and diverse beaches you've just got to visit.