Sea Woods is a large condominium complex located between S Atlantic Avenue and the Mosquito Lagoon Aquatic preserve. Unlike many condos that are built as high-rises, those here are one and two-story units spread out over a large area and covered in shade trees. Being between the lagoon and the ocean keeps the cool breezes flowing almost all summer long.
The beach is across A1A and it's only a short walk, but you will have to cross this busy road which is bustling with activity during the day and late into the evening. As long as you pay attention to the traffic and use the crosswalks, you should be fine. Be sure you keep your dog on a tight leash as there tends to a be a lot pedestrian traffic at certain times of the day as well, during rush hours when local and tourist traffic cause extra congestion.
The one thing you will have to get used to living in this area is the sheer amount of traffic that flows along A1A every day of the week. A1A is the main artery, not only here in New Smyrna Beach, but all the way down the east coast of Florida. While most of the heavy commercial traffic uses I-95 and US-1, this highway sees its fair share.
With so many condos in the nearby vicinity, you can also expect to see a lot of pedestrian traffic going to and from the beach and the few restaurants and stores within walking distance. Unless your dog is very well socialized and is used to dealing with both heavy vehicular and pedestrian traffic, you should try to gauge the quietest time of the day to cross over to the sand or stick to walking around the residential areas where the crowds are much quieter.
The entire community sits among shade trees which make it a lovely place to walk around. Alternatively, you can venture to the beachfront. Here, you and your dog can maximize the value of your exercise by using the soft sand for the outbound leg of your walk. On the way back, use the water and wet sand to enjoy the gentle warmth of an early summer morning.
On the other side of this area is the Mosquito Lagoon Aquatic Preserve where you and your dog can enjoy a different kind of green space. While there are organized boat and canoe tours, they are not dog-friendly. If you and your dog want to do a little exploring of your own, all you need is a canoe, life jackets, and a tracking GPS to help you find your way back. There is plenty to see here including many water birds and the resident pod of dolphins.