Lindberg is a mostly undeveloped area next door to Ward Higbees Trope Grant. Most of the structures here are businesses, but there are a few large homes along the railroad track and on the other side of it along the Indian River North. Directly on the other side of the river is the New Smyrna Beach Municipal Airport, so expect to deal with a small amount of air traffic coming in and out on a daily basis.
Besides the noise caused by the airport, Lindberg is a very quiet area of town that is far enough out from the center of town, but still close enough for you to reach the amenities you need within just a few minutes. This, of course, includes pet supply stores where you can buy your dog their favorite brand of food, toys, and treats. There are also plenty of restaurants nearby for your human tastes.
The is one of the quietest communities in town with a small amount of traffic feeding the businesses in the western half of the neighborhood. You might also find that rush hours tend to be a little busy and there is an FEC track running through the middle of the area. Once again, much like the airport noise, you and your entire family will need to get used to the noise of the trains passing through.
The residential areas are heavily wooded with limited access. The few roads running to and through the area are heavily shaded and don't have sidewalks for the two of you to walk on. Keep in mind that the mixtures of shade and sunlight can make you and your dog hard to spot when you are out walking. Be sure you stay in sight of oncoming traffic or opt to walk in less busy parts of the neighborhood.
The residential areas are heavily wooded and there are large areas of grass to the east of the railroad tracks where you and your dog can go for walks. To the west is Ward Higbees Trope Grant, which is another vast area of woods filled with trails to explore. The forests also offer you a shady place to walk that is a few degrees cooler.
A little to the north is at least one entrance to the Doris Leeper Spruce Creek Preserve. This is a nature preserve covering more than 1,600 acres of swamps and forests. There are numerous lakes, creeks, and tributaries that are home to numerous species of fish and waterfowl. There are also miles of trails to hike along, some of which will take you all the way to Rose Bay and back again once the two of you are up for the long hike.