Ashtons is a tiny area consisting of St. Paul's Episcopal Church and its outbuildings set in a mixed residential-commercial area. For next door neighbors, you have a strip mall to the north, a few fast food restaurants and an apartment complex to the west, and a large residential area to the east. The main road running past is the S Dixie Freeway which tends to be a bustling highway with plenty of truck traffic.
The majority of the nearby restaurants are fast food, but there are plenty of sit-down restaurants within driving distance for you to sample. You are also within a two-block walk of the Indian River North where there is a path running down to the water. There are several parks of various sizes in the area to take your dog walking in and, of course, when it gets hot in the summer, you can take them down to the river to cool off.
Because of its proximity to the highway and a strip mall, the area tends to have a lot of vehicular traffic at all hours of the day and night. While crime is generally low in the area, given the amount of transient traffic, you might want to keep your walks to the daylight hours.
The flat terrain has very little to offer in the way of strenuous exercise for you and your dog, but with a little creativity, you can at least keep your walks mildly interesting. Try to keep your walks closer to the river rather than the highway. This will keep the amount of traffic you have to deal with down to a dull roar and should eliminate most of the foot traffic.
There are plenty of residential blocks for the two of you to walk around to help keep your strolls fresh and interesting!
While Ashtons may not have much in the way of green space, there is plenty nearby for the two of you to enjoy. Directly across the Indian River North is Mosquito Lagoon Aquatic Preserve. Primarily a vast area of waterways, there are a few places to step ashore and go walking. The highlight of the preserve is the family of dolphins who has made the lagoon home for many years.
A little further north is the Spruce Creek Preserve, a nature preserve covering more than 1,600 acres of forests, wetlands, and waterways. The preserve also has a boardwalk that runs for 536 feet to the trailheads. From here, you and your dog can hike the three miles of trail that takes you past an observation tower that lets you see forever and all the way to the Rose Bay. It's a great place for biking, hiking, horseback riding, picnicking, and wildlife viewing!