Exeter's Royal Albert Museum in Queen Street is a fascinating place. You can get information sheets with quizzes and notes for things to look out for. The bonus is that it's FREE to get in! This would be a good half-day activity, leaving the rest of the day to browse around the shops or visit the Underground Passages, the Historic Quay or to walk along the River Exe.
Honiton’s Allhallows, High Street, Honiton has an excellent display of Honiton lace. Learn about this important trade and see beautiful examples of the lacemaker’s work.
Find out about the history of Seaton at the Axe Valley Heritage Society's display in the Seaton Town Hall, Fore Street, Seaton
Sidmouth Museum, Church Street, Sidmouth gives an excellent overview of this lovely Regency Town. There are some excellent local historians in Sidmouth and you will find all kinds of things to interest you here, particularly the work of Peter Orlando Hutchinson a Sidmouth artist and historian.