I live just north of Bury St Edmunds if you head out that way there are lots of neat things to do(heritage sites, antiques, pubs, Cambridge is about 30 minutes drive from Bury). Norwich is good as well and the surrounding villages are pretty neat with decent walking if the weather is nice. If I had to suggest one thing, I'd just say get a train on your off time to Cambridge and check it out. Very accessible and many amazing pubs. http://www.kingston-arms.co.uk/
IF you end up that way, definitely go here at least for a pint. If you need more recommendations let me know. I can ask my wife for recommendations for stuff around Norwich as well.