The Tri-Taylor neighborhood is a large square neighborhood near the center of Chicago, bordered on one side by West Town and on another by East Garfield Park. This neighborhood is not far from the bank of Lake Michigan. It encompasses several small parks, including Addams Medill Park, with grassy expanses that are perfect for playing ball with your dog, and Arrigo Park, which offers plenty of forested areas to stroll around in.
For more extensive trails, you can head towards Ping Tom Memorial Park and the tree-studded areas that are available for your wandering enjoyment with your pup. This park borders the Chicago River so you can feel confident of enjoying water views and the breeze from the river. If you head towards the bank of Lake Michigan, you can explore Grant Park and the shoreline here. While most of this park is for recreational sports, this is still a very large area to stroll around with your dog.
The Tri-Taylor neighborhood is quite pleasant to walk around as there is a divider between sidewalk and street that is under some comfortable shade. Despite this, you will generally find yourself walking your dog close to your side throughout most of this area due to lack of space to share with other passing pedestrians.
Garibaldi Park offers lots of areas for you to explore with your dog, as well as nice benches for you to sit and relax when you run out of steam. Arrigo and Vernon Park both offer much of the same where you can play a ball game with your dog or just enjoy the open space. If you head towards the water, you can enjoy walking along the Chicago River at Ping Tom Memorial Park. Northerly Island offers some natural shoreline where your dog can test her footing, though these greener spaces require some appropriate preparation. Bring plenty of water and the right footwear to keep yourself hydrated and safe throughout.
There are lots of green spaces available to the Tri-Taylor neighborhood so that you can extend your exploration beyond neighborhood walking. Lots of regional parks including Addams Medill Park and Arrigo Park provide unfenced fields and other spaces that are appropriate for exercise. These parks may have different rules regarding where dogs can and cannot go, so double check before you travel.
While you are unlikely to see significant wildlife in these well-maintained parks, it is possible to meet plenty of other people and pets as they enjoy their own outings throughout the day. Ping Tom Memorial Park offers enough natural area along the water to provide a home for more significant wildlife if you're more interested in that. You have a wonderful chance of seeing all sorts of migratory and residential bird life in this park, as well as having a good chance of seeing other nocturnal creatures when the sun begins to go down.