I have a 4 year old and live in La Grange so I think I can help
Bring the family and your grandson to the Farmers Market on Saturday morning (8 am-1 pm) and we'll give him a cookie at our booth (it's the one with all the glass cookie jars). Perhaps my son will be up there so they can play together on the green! The Treasured Child is a must - they are encouraged to play with all the toys. Great train table! Sweet on LaGrange is across the street and they sell BlueBell Ice Cream by the scoop, also KY Proud products like my friend KP's hot sauces and spicy nuts. Karen's Book Barn is another good stop with kids, they have a Lego table in the back near all the kids books, we get my son "cold coffee" there (aka chocolate milk with whipped cream). I would strongly recommend Norma Jean's for dinner; my kids have always been welcome there and the food (including the kids menu) is delicious.
La Grange is a wonderful town and very kid-friendly. There are some great playgrounds just slightly off the beaten path, so if you need more details, PM me. Hope you enjoy your visit!