For a nature-focused break, check out the Little Sugar River Farm, in Wisconsin. It's about a 2-3 hour drive from the city. www.littlesugarriverfarm.com
It's a little organic farm, surrounded by a nature preserve. The owners live on the property too, but not in the house/barn that you can rent privately. It's self-catering, but "Farmer Frank" will also cook you dinners upon request, usually using produce from the farm, and meat from local farmers. You can also use any produce from the farm for your own cooking, and he has some free range hens that provided us with delicious eggs for breakfast. Frank cooked us a delicious lamb meal one evening, and we actually made the drive to the farmer to pick it up. It was great seeing where our meat came from (although it was pre-butchered!) and that farmer took us on a little tour of his place too.
My husband and I had a mini-break there a couple of years ago and it was so refreshing after the city. This was pre-baby, so just the two of us, but we did think it would be a great place to take kids one day that didn't focus on 'things to do' and 'entertainment'.
There are bikes you can take for rides through the nature preserve - we ended up in a little town where we ate Amish Cream Pie at a diner that came straight out of a movie. And the pie was so good we ordered one to take home on our way out of town.
I'm not sure if it's what you're looking for, but it would definitely be a low-key, nature-focused, private family time, not a lot of hustle/bustle.