This state park, an hour north of Atlanta, is known for two things. One is the 729 ft waterfall (one of the 7 wonders of Georgia). It's the highest waterfall in Georgia and from at least one source, it's the highest cascding waterfall in the US east of the Mississippi River. A few miles up from the visitors center there is a parking lot just below the falls. From there is a trail up a wooden staircase that takes you immediately in front of the falls (great view of the falls), from there the staircase goes up to the top of the falls. With about 600 steps it gets kind of tiring.
The second thing this park is well known for is the Appalachian trail. A trail that goes up the easter states, about 2200 miles to Maine. Every year many ambitious hikers start their journey here. Most start their hike here, 8.5 miles away from the start of the Appalachian trail.
This is where through-hikers of the 2,175 mile long Appalachian trail start their journey. The actual start of the Appalachian trail is 8.5 miles away on the top of Springer mountain, but most people start here. Most through-hikers (and you'll notice them because they'll be carrying 40 pounds worth of equipment on their backs) start in early spring so that they could make it to Maine before it gets too cold. It's a nice hike, through wooded areas, but it's one way so if you're not planning on continuing on to the Appalachian Trail, you'll have to make turn back on the same trail.
If you're lazy or if you don't have much time (I'd like to say my case was the latter) you can get much closer the start of the Appalachian trail at the top of Springer mountain by car. It is about a 45 min drive (last 6 miles is a dirt road) from Amicalola Falls State Park. There's a parking spot next to the Appalachian trail, 0.9 miles from its start. The trail towards the peak is across the street from the parking lot. The hike is easy and quick. There's a couple of plaques indicating the start of the trail (and the fact that there's 2,175 miles to go to the other end), as well as a register at the top. Also, there is a great view of the surrounding areas from the top. There are no fees.
Amicalola Falls State Park contains the unofficial beginning of the Appalacian Trail. The 8.3 mile approach trail begins in near the Amicalola Lodge and heads to the top of Springer Mountain, where the AT begins.