Not sure of the age of children you are taking but, if you are talking about bank fishing in Greer/Taylors. The pickings will be kind of slim unfortunately, unless you know someone with water front property.
You can check out Lake Cunningham. It has pier access that leads to the water. I have only been there once to check it out. There were a couple of people fishing off the pier. It's a rather nice pier as well.
You can head on over around the corner and check out Lake Robinson. It has bank and pier access. Although, there you will need to head to the office to get a permit to fish on that lake outside of a regular state fishing license.
If you are willing to drive a little further you can check out Pleasant Ridge up off HWY 11. This place has multiple areas to choose from to bank fish and not quite as congested as say Robinson can be on a weekend.
You could take a short trip to Paris Mountain State park not too far from Greer. Good fishing access there as well at the entrance lake. There is however, a five dollar entry fee per person. Not sure if that includes children, I assume it does.
All of these waters you can find Bass, Breem, Blue Gill maybe even trout in the colder areas. That's what I have at the moment. Maybe someone else can chime in and give some suggestions because I would like to know also. I'm always looking for a good fishing spot. Fortunately, I know a few people that will allow me to fish on their private properties when I don't feel like loading up the boat and heading out somewhere. Good luck! Teach those kids how to pull in the fish! As they say, a bad day of fishing is still better than a good day at work.