Wymondham's a great place for people who like free stuff, and only a short trip outside of Norwich on the A11.
There's usually a free exhibition at the arts centre
And some nice walks (free to download here)
A good tourist information (the staff are really helpful and friendly) is in the Market Square in the building here:
The abbey is also lovely and free to explore (website)
And ff you're driving, don't forget to stop off at the Waitrose for your free tea / coffee