Woodelf, I love your questions (and I enjoy answering them) but you sometimes leave me a little confused because I'm wondering how someone who is blind can enjoy glorious skies? Or perhaps you've got a secret companion whom you've forgotten to mention in your previous posts?
My reference to a possible companion isn't just out of idle curiosity. If you're planning on visiting East Anglia on your own it would presumably be helpful if the location was reasonably close to a railway station but that's obviously unimportant if somebody else will be driving. (Actually, having read about all of the other things you do, I wouldn't really be too surprised if you told me that you were planning on driving to Norfolk on your own!).
Holt, as mentioned by Echokilo is a delightful town, with a very 'upmarket' feel to it. While it qualifies as a 'country town' it's not really 'countryside' so I'm not sure whether it meets with your requirements. It can be accessed by rail by taking the National Express East Anglia train from Norwich to Sheringham and then going to the adjacent Poppy Line station for the journey to Holt, which is often steam-hauled.
Holkham is a very pleasant coastal village. The Victoria Hotel has a good reputation and is in easy walking distance of the beach (although getting there does involve crossing the busy A149 coast road).
Burnham Market is another really nice little town in North Norfolk. The Railway Inn has lots of good reviews:
http://www.hostearms.co.uk/Railway/
However I hate having to recommend anywhere in Norfolk. To get there from Basingstoke you'll have to go through a far finer county, Suffolk. Can you guess where I live?
;-)
Chris