Marynook is a lovely neighborhood to walk through with your dog on a loose leash. Homes are closely spaced but they are set back behind little grassy yards that are rarely fenced. Homes have unique architectural design and attractive landscaping while intermittent mature trees provide pleasant shade on hot Chicago days. Within the park area, there is a small separate community with two or three story townhomes. If you have access to this gated community, it is a lovely place to walk your dog on a loose leash as there is very little traffic and the terrain is mostly flat.
Avalon Park is a great place to walk on the pleasant trails under mature tree cover or enjoy an on-leash game of fetch. If you want to explore more wilderness than the city park, Van Vlissingen Prairie is a short car trip south and offers a wide variety of terrain including forest, grassland, and ponds.
If you follow the prairie south, you will find the Railroad Marsh which has a nice path through marshy terrain. South of this area is Marsh Park and The Harborside Marsh Pond. All of these areas offer your dog a unique opportunity to test their footing in marshy terrain. Lake Calumet is a gorgeous area to explore as well, especially the West Shore and Gull Island where you are guaranteed to see exciting bird life.