Don't rule out Norwich!
Much as we Ipswich folk (who have an intense rivalry with people from Norwich) hate to admit it, Norwich is actually rather a nice place.
As has been mentioned, it's got a good market (which is incredibly cheap; there aren't may places where you can get tea or coffee for 50p these days!). It's got plenty of shops, which include lots of small independent ones as well as the big names that you see everywhere else. It's packed with history and their are plenty of good restaurants and pubs.
Fred mentions a lack of nightlife. That might we'll be true if you're into clubbing (although the riverside developments, close to the rail station, seem to offer plenty for younger people to do) but Norwich has some of the best theatres in the country.
Norwich is also a great base for exploring, with the North Norfolk coast and some lovely little market towns all close by. (If you fancy a drink or two while out on your travels, go by train. A day's unlimited rail travel, throughout the whole area, costs £16 with an Anglia Plus ticket, which will take you to places like Ipswich or Cambridge, or out to the coast).
http://www.visitnorwich.co.uk/