Right in downtown Fort Mill (on Main Street next to The Local Dish) is a cute art studio for kids with really neat things for grown ups, too - they have an "in house" coffee bar and sell art pieces, craft items and jewelry - you can sip coffee while the kids do art. I believe it's called United Artisans Studio. There's also Plaza Fiesta near Carowinds, and they have a GIANT "habitrail" for kids. It's only a couple of dollars for them to play on it. And they sell churros and ice cream! A few good eateries, too. Not as many vendors, though. It's like a giant flea market, but I hear there's new ownership and they upped the rent, so a lot of vendors left. Still a neat place, though. I believe on Saturdays they have live music during the day.
You can also take a ride to Lazy 5 Ranch in Mooresville. So neat! The kids could feed the animals. Lots of fun!
North Carolina Animal Park | Lazy 5 Ranch
Riverbanks Zoo is really fun, too, like the previous poster mentioned - but it's more like an 1.5 hours from Fort Mill.
If you don't want to spend a lot of money - Carmike Cinema on Cherry Road (dollar theater) is playing Hotel Transylvania. Funny movie!
If the weather's good - you can walk around Glen Cairn Garden.
Glencairn Garden
Just some ideas!