The Parsuns to Cocoa Beach neighborhood consists of single-family homes sitting along South Orlando Avenue and between 6th Street and 7th Street. Directly across the street is the massive Oceana of Cocoa Beach condominium complex that stretches for two full blocks. Behind you and to the east is a selection of luxurious single-family homes and townhomes before you reach the beaches.
For shopping options, a short drive to the north will take you to the West Cocoa Beach Causeway, the central shopping district on this side of the river. There are several stores, including a Winn-Dixie Supermarket where you can stock up on food and treats.
You can walk to the beach from your home or hop in the car and be sitting in the shade at the local dog park in less than ten minutes. Most of the beaches here are open to dogs during set hours, giving both of you the opportunity to enjoy them.
South Orlando Avenue tends to be a reasonably busy street during the day with the heaviest periods of traffic being the morning and evening rush hours. Since South Orlando is also Florida State Highway A1A, a major north-south route all along the east coast, you will find that traffic never completely dies off. There is a sidewalk on the other side of the road for you and your dog to use for your daily hikes, but you will have to cross the busy highway first. Keep in mind that there are no real changes in elevation, at least, to make it just a bit easier to wander this neighborhood.
Although not all of the streets around you have sidewalks, it won't take you long to find out where they are so you can plan your walks out in advance. Alternatively, you could walk one block east and use the wide sidewalk running along South Atlantic Avenue. It's a lot wider and runs continuously for miles.
One block west is Ramp Road Park. This park offers playgrounds, tennis and basketball courts, and plenty of grass for you and your dog to run around on. It's conveniently close and well-kept, making it an excellent choice.
Then there is the beach! It's only a five-minute walk to the east. You and your dog are welcome on most of the beaches during a few set hours. The two of you can hike for miles, using the soft dunes for a workout and the wet sand for relaxing strolls.
If you are interested in an off-leash dog park where your pup can safely run around, the Cocoa Beach Public Dog Park is less than 2.5 miles north on North Atlantic Avenue. Covering three-quarters of an acre, the park offers separate areas for large and small breeds along with an area you can use to rinse your dog off and help cool them down.