What is there to do in Naperville that a 6 yr old and a 10 year old might like.
Naperville has a nice children's museum. The 10 year old might be a little old for it.
Naper Settlement is fun for kids.
I love to walk along the River Walk and have dinner in downtown Naperville. My favorite downtown eatery is Jimmy's since you can sit outside on the patio. It has a bar atmosphere, but fine for kids earlier in the evening. They might have fun visiting Naper Nuts & Sweets - it's an old fashioned candy shop. If they have high end taste, take them to Le Chocolat on Washington. It's expensive, so we limit ourselves to one piece! Sugar Monkey has good cupcakes. Gelati and Cold Stone Creamery are both on Jefferson. If they like books, you could take them to Barnes & Noble or Anderson's Bookshop - you could spend a lot of time browsing.
It's a bit of a drive, but our kids always liked visiting Kline Creek Farm and Cantigny.
If they like to ride bikes, the Fox River Trail isn't too far from Naperville. Even if they don't have bikes or you can't fit them all in your car, there are places in Batavia where you can rent bikes. There aren't too many street crossings, so it's fairly safe. Along the trail, you can visit Red Oak Nature Center and even get to see a cave and a windmill!
If you are here over the July 4th weekend, there is the Ribfest which has a carnival that kids will enjoy. IlliniTrav gave some great tips that should keep the kids busy. Our grand kids especially like the Children's Museum and Naper Settlement.