You may also be able to find larger and more formal gardens within a reasonable distance to visit. We are fortunate to have more than one close enough to enjoy on a regular basis. One that we visited recently is Sarah P. Duke Gardens. They always have something new growing there that changes seasonally. There is a pond that is abundant with wildlife including a variety of waterfowl, turtles, and fish. Even though it can get quite busy I can still hear the sounds of nature and smell the scents of the flowers growing there. It was especially uplifting to see the children interacting with nature.
I highly recommend for anyone who is able to visit a local garden, park, or natural area. Sometimes they are closer than you think and you may not even know they exist. You can do an internet search or talk to neighbors to see if they know of any. Local papers may have articles about these hidden gems in your community. Garden centers may even be a good source of information. The costs are usually low or even free in some cases and some areas are handicap accessible. I would do research before going to make sure they allow dogs and to be prepared for parking as well as any costs that may be associated.