Come and visit us here in East Anglia. You don't need to go via London if you're coming down the East Coast Main Line; you can change trains at Peterborough and then travel on the cross-country route.
Norwich is a lovely city to explore, with lots of history, excellent theatres and live music venues, great pubs and some top quality restaurants:
http://www.visitnorwich.co.uk/
Further, it's a superb base for exploring East Anglia by rail. £36.20 (reduced by a third for railcard holders) gets you unlimited travel for any 3 days out of 7 across Norfolk, Suffolk and much of Cambridgeshire. (Travel has to be after 0845 on weekdays - although there are some trains you can use earlier - or at any time at weekends or bank holidays):
https://www.abelliogreateranglia.co.uk/tickets-fares/discounts/rangers-rovers/anglia-plus
So you could explore the Norfolk coast (Sheringham and Cromer are both very pleasant) or towns like Ipswich (don't miss the waterfront area)
http://www.allaboutipswich.com/
and Ely:
http://www.visitely.org.uk/attractions/where-visit
as well as historic Cambridge:
http://www.visitcambridge.org/
(In both Ipswich and Norwich you can use your Anglia Plus rail tickets for travel between the rail station and the town/city centres as well).
If I can't tempt you to come to East Anglia (WHY NOT?) I'll still mention that there are lots of rail rover and ranger tickets available elsewhere across the country but they're
very poorly advertised. However you can find a full list here:
http://www.nationalrail.co.uk/times_fares/rangers_and_rovers.aspx