Redland is a tiny mixed section of businesses and residences along Highway 1, A1A, and the North Dixie Freeway. On the other side of the highway is the Spruce Creek Preserve. From this point on the highway, you are one of the last neighborhoods before the highway takes you through the preserve and into Port Orange.
Although there is only one restaurant, you are only ten minutes from downtown New Smyrna Beach where you should have no problem finding plenty of great places to eat, grocery stores, pet supply stores, and bars. Along with this, there are the bridges that take you over to the beachside and the waterfront along with miles of sand to hike on with your pup.
There are several other parks and green spaces for you and your dog to go hiking and playing in. The one thing you'll have to deal with is the noise from the highway which you will soon get used to.
The combination of US Highway 1, A1A, and the North Dixie Freeway is the major non-interstate highway running from far up in Maine all the way to Key West. Because of this, you can expect traffic to be flowing 24 hours a day with the daylight hours being very busy. Luckily, you can use the streets back away from the highway for your walks. Some of them have sidewalks while others do not.
The ground here is flat, but with the preserve within walking distance, the two of you shouldn't have much of a problem finding plenty of places to go hiking. Be aware there are several businesses in the area that will add to the traffic, so finding ways to stay away from the main highway will make your walks safer and more enjoyable.
The community of Islesboro is just to the southwest and offers plenty of residential blocks to incorporate into your walks for a little variety.
The nearest green space is on the other side of US-1 and is known as the Doris Leeper Spruce Creek Preserve. The preserve covers well over 1,600 acres of forest and swampland. More importantly, the park is full of trails for you and your dog to hike along in the shade. The trails take you to Rose Bay and back and are very popular with hikers, cyclists, and dog walkers. They tend to be busy at various times of the day, but it won't take you many walks to find the quietest times to go hiking.
The other green space to think about walking your dog on is the beach. It's less than fifteen minutes away and offers you soft sand that is hard to walk on and gives you a great workout. When your leg muscles start to complain, you can turn around and make the return trip on the firm, wet sand. Your opportunities are endless!