Lots of nice places … I’ve lived here all my life.
North norfolk coast – Brancaster, Burnham market, Wells-next-to-sea, Holkham hall, Sandringham, round to Sheringham (which has a pedal loop, and a few short but fun trails if you do decide to a bike)
East norfolk coast – Winterton is popular for dog walking, lots of sand dunes to explore and a good mobile cafe. If you have kids you can brave Great Yarmouth for a night at the arcades.
South norfolk – Southwold/Aldeburgh, although personally not a fan.
Norwich – good for a night out, lots of places to eat/drink, good restaurants/bars on St Augustines street and the laneways.
Good pubs around the area – The Pigs, White Hart Hingham, The Lion Thurne, Gin Trap … there are lots of good pubs.
Wroxham – go hire a boat and get out on the broads for a day, it’s lovely with frequent pub stops along the way.
Thetford forest – it’s ok, there’s no elevation, so it’s all pedalling, I take my rigid 29er and it makes it a bit more fun.
Norfolk has lots of waterways so if you have a paddleboard/kayak/canoe it’s ideal for that.
Holkham beach and the Victoria pub opposite it.
Sadly it’s no longer a pub, but accomodation/restaurant. Wells is close with some good pubs.