One day is plenty of time to see all the attractions in Decatur. The best days to visit are Tuesday through Friday; as the Jesse Owens Museum and the Carnegie Visual Arts Center are closed on Sunday and Monday, and the Old State Bank and Oakville Indian Mounds are closed weekends seasonally.
You should begin your tour in Mooresville (free). This town dates back well before the state of Alabama was admitted to the United States. President Andrew Johnson worked here as an apprentice in the tailor trade. With historic buildings throughout the city, this makes a nice place to start your day as you can see buildings dating back to the early 1800s.
Next, drive south to Decatur. You can visit the Old State Bank first (free). This site will give you a brief overview of the pre-Civil War area as well as the use of the town during the war. This attraction opens at 9:30am, so leave Mooresville by 9am to be here for the first tour. The guided tour will take you to all the rooms in about one hour.
Within walking distance is the Civil War walking tour of the city (free). This walking tour will take most people about one hour and you'll see the biggest Civil War battle in northern Alabama, excluding the combined skermishes between Forrest and Streight that crossed the entire state.
Next, walk to the Carnegie Center of the Visual Arts (free). Depending on the exhibits that the center is showing, seeing this attraction will take you an average of one hour. It is pretty small, so you can take your time and see all the exhibits thoroughly.
The Cook's Natural Science Museum (free) is just a short drive from the Carnegie Center. Start your visit with a film that shows how insects act in the wild. Then, you can walk through the exhibits of rocks, insects, and mammals from the area. The entire attraction should take about an hour.
Next drive south to Danville. Here you can see the Indian mounds. Depending on your interest and how long you spend walking on them, you can see the mounds and the museum in about an hour (free). You need to finish at the mounds by 2pm to get to the Jesse Owens Museum with enough time to see it before it closes at 4pm.
Next, move to the Jesse Owens Museum and Memorial Park ($5). You should spend a couple of minutes outside the museum seeing the recreation of the home that Jesse Owens grew up in, the statue to the Olympian, and the Olympic torch that burns in front of the building. Inside the museum, you can see the Olympic jerseys. There is also a wonderful film in which Owens chronicles the events of the 1936 Olympic Games, which lasts about 50 minutes. The museum is only open from 11am to 4pm from Tuesday to Saturday and 1pm to 4pm on Sunday, so plan your time to see this attraction while it is open. If you go off season, you should call a couple days in advance to schedule your visit as the museum is run by volunteers and is often closed during slower periods regardless of the posted hours.
Finally, drive back north through Decatur to Athens. Here you can see the Houston Memorial Library, Athens College, the Donnell House and the Limestone County Courthouse. At the courthouse, you should note the memorial to Confederate soldiers, the memorial to General Forrest's victory here in Athens and the plaque that represents this court houses modern historic significance (a case that spurred the Civil Rights movement). All of these are outside only exhibits, so you can see them as long as lighting permits.
You should be complete with all these attractions by sundown and can head back to Decatur or your next destination for a nice dinner before ending your day.
Total cost of the trip is $5, plus food, gas, and lodging.
I recommend a day trip to Decatur for anyone interested in history and for families with children. Also, this trip is nice for frugal travellers as all the attractions except the Jesse Owens Museum are free; hotels are cheaper as this is not a major tourist destination.