Plenty of coastal interest, lots of heathland around thetford where the gorse/heather can be interesting. your not going to get dramatic mountains and grand visits but more selective shots, Essex is similar unfortunately but then thats what holidays and weekends away are for, just dont tell the Mrs.
I'm off in the East of Norfolk. The challenge as others have amusingly noted is it's pretty flat, but that's not the end of the world. There's lots of water about.
I've taken some beach and marsh images (and seals) I like at Horsey beach, The Windpump is also pretty and I think they've finally finished the restoration but it tends to be a busy tourist spot.
I've taken more beach pictures up at Holkham, while it's pancake flat the massive beach can have a really beautiful light.
Out on the broads there are various windmills and windpumps that can add a focal point for an otherwise flat scene - look at St. Benet's Abbey.
Castle Acre is worth a look as is Baconsthorpe castle.
Norfolk's great. Beautiful coastline especially the North, quite a lot of windmills/windpumps and waterways. Broads pretty especially in winter if there is frost or mist. Look out for poppy fields and barley fields in the next few weeks (barley looks great being blown in wind). Justin Minns’ book is a very good start
I can't think of much in central Norfolk, but it's not far to the broads or the north coast, both of which are full of landscape opportunities.
A few old ruins around too (Castle acre, has both a priory & remains of a castle...) which can work very well.
Not the right part of the world if you want to shoot mountains, but as long as you avoid the fens it's not exactly flat.
My parents lived in Dereham (which apparently includes the exact geographical centre of the county). Wells next the sea & Norwich were both within 30 minutes drive, with lots of good locations near both.
I'm in Norfolk too, only been here for a few months, but I bought the "Photographing East Anglia" book by Justin Minns. Huge number of places to go, the book has just as many places as the Scotland book (which I also own).
Sure, there's no mountains, but there's miles and miles of coast, tonnes of forest/woodland, lakes, rivers, cliffs, dunes.
East coast locations for sunrise and west coast (Hunstanton/Heacham/Snettisham) for sunset.
The marshes around places like Blakeney and Burnham are good.