With four kids, I could spend a fortune in extra-curricular activities. Fortunately, Metro Parks and Recreation offers many free and/or cheap classes at many community center locations throughout Nashville. The four main areas of interest are visual arts, dance, music and theater. This link will take you to the current schedule (only a few weeks left for these classes.)
However, the word is that the new schedule should be posted some time in April and I believe that classes begin in Late May/Early June. Keep checking.
For anyone outside of the Middle Tennessee area, take a look at your local "dot-gov" page to see if you have a similar program.