Nottingham makes a good base for the East Midlands and the southern Peak District. Sherwood Forest — what's left of it — is a half-hour drive north and home to the Major Oak, the ancient hollow tree where Robin Hood is said to have hidden. Newstead Abbey, the ancestral home of Lord Byron, is just south of the forest and worth a visit for the grounds alone. The Peak District proper starts about an hour west of Nottingham; Matlock and the gorge at Matlock Bath are the obvious targets for a first visit.
Lincoln is an easy day east — its cathedral is one of the finest in England. Derby is twenty minutes by train and gives access to the Derwent Valley Mills, a UNESCO industrial-heritage site, and to Chatsworth House.