Checking out Logan Square. Are there any areas with more nature?

I finally made the leap. Last night I landed at O'Hare and found my way to a place to stay overnight. I'm in the Logan Park area. It is a cool area, but I'm wondering if there is a neighborhood that has a bit more nature? I miss seeing trees and I wonder if there is any place to hike or take long walks. Still tired from travel. I swear I could use just a few days to sleep.