Bellair Shores may not be quite on the shores of the Atlantic Ocean, but it's pretty close. It is, however, right next door to Bellair Plaza, one of the largest shopping complexes on the beach. Anchored by a Publix grocery store, there are several other stores here as well. You are also just down the street from Seabreeze High School and a ten-minute walk from the beach. If you like to dine out, you should plan a little extra time into your meals as you need the time to drive to the nearest restaurants.
The nearest park is more of a car park than a place to play, but the Andy Romano Beachfront Park does have some grass and gives you direct access to the beach. You are definitely close enough to the beach to make the most of the summer weather, but don't forget that you and Fido can go for walks on the sand all year round!
The immediate terrain is typical of what you might expect in a suburb you could find just about anywhere in the country. The only big difference is the amount of sand you have to live with. There are plenty of sidewalks for you and Fido to hike around the neighborhood and several others if you prefer walking on something solid.
If you choose to stick to paved surfaces, be sure you check your pup's paws for signs of damage frequently as the rough surface can wear through the skin. Staring with short walks, at first, will help their paws to develop a thick layer of callus that will prevent damage.
The beach offers a much better challenge in that the dry sand can be very challenging to walk in, giving everyone a great workout. When you are at the far end of your walk, you can turn around and head home on the wet sand, cooling your feet in the surf.
The nearest usable green space is, of course, the 23 miles of beach running along the coast of the Atlantic Ocean. The beach offers two different types of terrain, plenty of space to walk, jog, or run, and lots of fresh air and sunshine. The best time of day to hiking along the beach is early in the morning when there aren't many others out and the summer sun hasn't hit the point at which it's too hot to tolerate.
If you would prefer to take a little time walking in the shade, the two of you can cruise north on Beach Street over on the mainland side. This will take you to Tomoka State Park, home to the headwaters of the Tomoka River and the ancient Timucua Indian village of Nocoroco. This village was built here because the ponds, lakes, and river were teeming with fish, providing easy to catch nourishment for the village.