Not quite Norwich, but close enough. Climb the 89 steps and two ladders to the top of St Helen's Church at Ranmoor for panoramic views of the Norfolk Broads. There is a 'suggested donation' box.
Also of interest at Ranmoor is Ranworth Broad and Nature Reserve, which has a Wildlife Centre run by Norfolk Wildlife Trust (check the website for opening times)
http://www.broadsideparishes.org.uk/visitors/ranworth_tower.htm
http://www.norfolkwildlifetrust.org.uk/ranworth.aspx