Cinemark Tinseltown Theatre at Exit 7 in Bristol has a summer movie program on Wednesdays at 10am. Admission is only $1!! Check out the link below for the movie listings for each week.
The Cinemall here in Abingdon also has KidToons on Fridays, Saturdays and Sundays at 11:30. There is a link to the right under "Things to do" for it.