The Shore Villas Condo is on A1A and S Atlantic Avenue right on the beach. You can watch the sun coming up over the Atlantic Ocean as you take your dog for their morning walk. At the end of the day, you can watch it set as it slides down into the waters of the Mosquito Lagoon Aquatic Preserve.
One thing many who live here like about being this far south is the lack of crazy tourist traffic. While there is some, it's nowhere near as busy as the central part of town on the beachside. The same applies to foot traffic both on the sidewalks as there isn't as much to do here. That is until you get to the beach where you are likely to run into lots of people enjoying the sun and surf. The best way to avoid the traffic here is to take your dog out for walks early in the morning
This is a predominantly residential area of New Smyrna Beach with several condos lining the beach and plenty of single-family homes between A1A and the Mosquito Lagoon Aquatic Preserve. While you might not see quite as much traffic this far from the center of town, you still need to keep a close eye out while walking your dog along the A1A if you decide to cross over to the residential areas to go for walks.
The hard part is getting from the condos to the sidewalks as you must cross over a large area of tarmac parking lot on your way there during the summer. In the summer months, the pavement will be hot enough by midday to burn your dog's feet. During these months, you should be taking them out in the morning before things heat up. You may also find that sticking to hiking on the beach where the sand is nice and cool is preferable.
The nearest green space is right outside your door and covers many square miles. You can take a swim in the waters of the Atlantic or, if you are into serious hiking, you could follow the dunes all the way from the Ponce Inlet down to the Canaveral National Seashore and Kennedy Space Center.
On the other side of the peninsula is the Mosquito Lagoon Aquatic Preserve. Covering thousands of acres, the preserve is part of the Indian River Lagoon System. The fishing here is spectacular and the scenery excellent. The one issue is that elevated landmarks can be very hard to spot, making it easy to become disoriented. Be sure you take someone with you until you are used to the area. Also important to note is that the only way to see the lagoon is by boat, but most dogs love going for boat rides, so hopefully yours does too!