Hi Carol, since you mentioned you prefer smaller roads, you could take Lake Shore Drive through Chicago
along the lakefront. It's scenic, but you go through the city.
If you're looking to avoid city traffic completely, a great alternative to the Chicago Botanic Garden
would be the Morton Arboretum
. That makes sense if you're bypassing downtown Chicago and staying on less busy suburban roads.
If you want to avoid highways from there, most people would take either US-53 or US-83 to go north on local roads that are still fast with fewer stoplights.