The Golf Cottages of Cocoa Beach can be found on the Minuteman Causeway next door to the Cocoa Beach Junior-Senior High School and the Cocoa Beach Country Club and Golf Course. The homes here are not precisely cottages, they are large luxury homes! You are close to the country club and the Cocoa Beach Aquatic Center, both of which are open to the public. The aquatic center even has a heated 50-meter pool, a spray park, and a waterslide.
There are several stores, gift shops, and restaurants along the Minuteman Causeway including a small grocery store for you to shop at. However, if you want a larger grocery store, there is a Publix less than ten minutes to the south on A1A within a strip mall complex. Further to the south, there is a pet supply store. Between the two, you should be able to find the supplies you need to keep your dog well-fed, happy, and healthy.
For some reason, there isn't much in the way of sidewalks for you and your pup to use when going for walks. Given that there are several residential communities out here on the island, the two of you will need to be careful when going walking. The traffic tends to be heaviest from 7 to 9AM and from 4 to 6PM. While you can take your dog out during these hours, you will be dealing with traffic that can be dangerous at times.
The one place you will find sidewalks is along Tom Warriner Boulevard. The east side of this road has a wide paved, flat walking trail the two of you can put to good use for your daily strolls. The path runs from the Minuteman Causeway all the way to the country club and past the water treatment facility and the Racquet Club of Cocoa Beach.
There are several parks within the City of Cocoa Beach where you and your dog can run about as long you keep them on a short leash and clean up any messes. While you are surrounded by a public golf course, this means it's open to those on two legs, but not to those on four legs for both health and safety purposes.
Luckily, there is one park in particular that is only ten minutes to the north on A1A that should be of particular interest to your pooch. The Cocoa Beach Public Dog Park covers a large area that is fenced-in and divided into areas for large and small dogs. The park has water for the pups, a rinse station, and plenty of chairs to sit while your pooch goes off and plays with others. The park also has direct access to the beach where you can go for long walks together.