Nearby 'attractions':
Amozonia Zoo
The Shire Horse Centre
The Steam Museum at Thursford
Musselburgh Military Museum (or something like that)
or
A ferry trip to see the seals at Blakeney Point (ferries leave from Morston - book in advance over the 'net or phone) if your autistic child would manage an hour's boat trip? The seals are almost within touching distance.
Go to Wells Next The Sea, where there is an indoor soft play place in the town, on the quay, or down by the beach trampolining, a boating lake, pinewoods to explore, and one of the best beaches in the country.
Cromer has a tiny museum, with information about the fossilised Mammoth found at West Runton. W Runton beach is nice, too. Further along the coast Brancaster has a lovely beach. And Holkham. But Wells, whilst being thoroughly wild and unspoilt, has access to ice creams and toilets.
Good cliff top walks from Cromer.
Crabbing from Blakeney Quay.
Rent a canoe on the creek at Blakeney.
Sheringham has a small theatre, and the indoor Splash pool with wave machines etc.
Cromer has a small but good multiplex cinema.
Sheringham Park is a nice NT place - outdoor walks through woods and spectacular rhodedendrons if you are there in June.
An hour and a bit drive to Bewilderwood.