Walking through Bronxville is absolutely gorgeous with the multimillion-dollar homes and extensive landscaping across the flat terrain. Homes are set far back from the road on giant lots. Some yards are devoted to wide grassy spaces while others have so much landscaping that you cannot see the home behind it. Most roads do not have sidewalks, but sidewalks are not necessary for these rarely-trafficked roads when there is so much grassy space to walk on if a car should come by. You will feel comfortable walking your dog on a loose leash or rollerblading, skateboarding, or bicycling with your dog throughout most of this neighborhood.
If you are looking for a change from the neighborhood streets, you can head west towards the Bronx River. The waterway is wide here and has lovely forest on either side. Trails run along both sides so that you can enjoy the views in comfort.
You may feel like you are in a park walking through much of Bronxville due to the large grassy lots and extensive landscaping, but for more natural exploration, you don't have far to go. The Bronx River borders Bronxville and has lots of lovely grassy and tree-covered spots around the river. The waterway widens in this area so you have an especially gorgeous view of it.
You can follow the river up through more lovely forest and grass until you get to Malcolm Wilson County Park. If you get hungry along your route, the Old Stone Mill is a very cool 1800s mill that has been turned into a steakhouse with beautiful outdoor seating along the river. From Malcolm Wilson County Park, you can continue to follow the Bronx River up for many miles of forested exploration with lovely views of the river and a walking trail along the whole way.