Briarwood is a single street running off of Mason Avenue next to the Westside Baptist Church. This neighborhood is near several shopping centers and a few fast-food restaurants for when you need a quick bite to eat. But if you want a family-style restaurant or a fine dining experience, you won't have far to drive as Daytona has plenty of both.
There is a sweet little spot nearby with a pair of lakes and a walking trail that goes around both of them for you to enjoy walking around. The beach is only a short drive over the Halifax River and you are close to several smaller parks to go walking in.
The lakes and grass will come in handy during the summer months when the temperatures are in the 90s. You can even go walking all winter long with temperatures hanging out in the 50s and 60s with the exception of January when it drops into the upper 40s.
Briarwood offers the typical suburban terrain with lots of streets and sidewalks, but not much else. The ground may be flat, but that doesn't mean you can't still find ways to make your walks with more interesting. For example, why not see how many blocks you can walk each day? Start out slowly and build your way up before going for distance. To make things more interesting, try going around a variety of the many blocks in the surrounding neighborhood.
Of course, you can also walk on the path that runs around the two lakes behind the shopping center. Doing this will at least give you a break from walking along the streets and you can enjoy watching the fountains.
Keep in mind that the pavement can become too hot to walk on for your pup. Check it with the back of your hand. If you can't hold it there for 10 seconds or more, it is too hot!
Beyond the lakes and grass behind the shopping center, there isn't much green space in the nearby area beyond a small copse of woods and a vacant lot. However, Derbyshire Park is only a short drive to the north and offers a number of sports fields and courts.
A little to the west of this park is the Cedar Highlands Park, a large forested area with trails to explore.
If you want a park for your pup to be able to play in without having to be tied to a leash, you can take the short drive out to the Halifax Humane Society. The public dog park here offers separate fenced-in areas for dogs of different sizes. There are water fountains for the dogs and their humans as well as places for them to sit in the shade. This is a great place for your dog to get out there and socialize with their four-legged peers!