The first thing is to decide whether you want a city or country break. For cities, Norwich is the obvious choice; a stunning city with plenty to do all the year round. or you could try a seaside town like Great Yarmouth; the East Anglian coast is spectacular and would be great for a weekend in summer especially. Or just type 'norfolk towns' in a search engine and do a little more research if you'd like to find somewhere less well known to tourists.
For a relaxing rural break, a lot of people like to stay in the Norfolk Broads. It's possible to rent a cottage in this area for two or three days, but the most popular option is to hire a boat and stay on that. if you click here and put in the days you would like to go, you can find plenty of weekend and short stay offers.