The Palmas De Majorca condominium complex sits along the beach, three blocks north of the Minuteman Causeway. Across the street from the condo, there is a small strip mall and then residential areas. On both sides of Palmas De Majorca, there are condos and hotels as far as the eye can see in either direction.
There are a few restaurants nearby, but if you need places to buy groceries, you are less than a five-minute drive from the causeway where you will find two local supermarkets, a few restaurants and small businesses, the Cocoa Beach city offices, the fire department, and the police station.
If you need a bigger grocery store, there is a Publix supermarket to the north at the corner of A1A and South Banana River Boulevard. Here, you should be able to find everything you need to feed your entire family. You shouldn't go wanting in this area of Cocoa Beach!
Living along A1A means having to deal with a significant amount of traffic from early in the morning until late into the evening. A1A is the coastal highway running along the east coast of Florida from a point just short of the Georgia state line until it comes to an end on Key West. You and your dog can make good use of the sidewalk running along the east side of the highway as the terrain in this region is flat and easy to traverse.
Alternatively, the two of you can cross the highway and take your walks into the residential areas on the other side of North Orlando Avenue. While you should probably avoid walking here during rush hour, the rest of the day should be relatively peaceful. In addition, there are plenty of sidewalks for the two of you to use that will help keep you out of the way of traffic.
If you and your dog go out the back door of the condo building, it will take you less than two minutes to be on the beach. Yes, here in Cocoa Beach dogs are permitted on the sand from 4th Street to the northern edge of Murkshe Park! Dogs have special hours when they are allowed on the beach, so watch for regulations to ensure you're following them! With your dog on a leash, the two of you can hike along on the wet sand close to the surf for as many miles as you can handle.
The city has provided pet waste disposal containers for your use, so you'll want to be sure to use them and help to do your part to keep the beaches clean. With the set hours that you can visit, you should be able to avoid the midday heat that tends to creep into this part of Florida.