J.K.
Hi J.,
There's a big pond just behind Home Depot that has sidewalks for running or walking and a playground for your little girl. It also has ducks that you an feed. It's a free alternative to some of the other activities mentioned. There's also Saluda Shoals Park. Drive down Lake Murray Blvd going towards the dam and make a left onto Bush River Rd. Saluda Shoals is off that road on your right. They have playgrounds there and a waterpark. It's a bit cold for that right now but well worth it in the Spring and Summer. You can also kayak/canoe/intertube at Saluda for future referrence. For the Fall, there's a pumkin patch/Hayride/corn maze farm in Gilbert. It's The Farmer's Shed, ###-###-####.
Have fun!