If you're fortunate enough to get out boating on the Tennessee river, try out the cliffs on the Morgan county side about half way between Ditto and Triana (pronounced "Try Anna" for all you non-locals). They're 30-45 feet tall. There's a rope swing and some people even jump off the cliffs into the deep water at the bottom.
Huntsville doesn't exactly have a real arts district, but if it did, it would be Five Points. This little old milltown is a nice mixture of different houses, little old shops, with a hint of counterculture punctuating the redneck culture.