I have wanted to visit this site for years, and am so glad that we finally stopped by. It was easy to find, and definitely worth driving a few miles out of our way. The bridge itself is a piece of history that you won't find anywhere else in South Carolina, and is surrounded by a lovely little park maintained by Greenville County. It is a beautiful spot for history lovers, photographers (we actually saw a professional photo shoot going on while we were there), and anyone who loves spending a few tranquil moments outdoors.
The bridge is located over Beaverdam Creek, which has some rocks on each side of the bridge that are perfect for going out into the water -- which is something I'm sure most kids will want to do. I would caution that they need to be well supervised, because we found some of the rocks to be quite slick on the day we were there. The ones upstream of the bridge offer a somewhat close-up view from below, which caused my 7 year old to quietly remark, "this is beautiful" when we got down there. That's not something you would normally hear from a little boy, so he must have thought it was pretty special!
There are also a couple of places to sit or bring a picnic -- but as other reviewers have mentioned, be aware that there are no restrooms at this site. You are pretty much "out in the middle of nowhere", so finding one at all might be a challenge if you need one.