Sea Monica is a small residential area less than one block from the beach. The houses here are a blend of single-family homes and townhouses in an area that is filled with condominiums. The neighborhood straddles Monroe Avenue and sits along Ridgewood Avenue, making it easy to get to, but resulting in some fairly busy spots.
For shopping, there are a number of tourist shops in the area and a few stores and restaurants along A1A. If you take A1A towards Cocoa Beach, you will find a Publix Supermarket where you can fill up your pantry with food for every member of the family, even the one with the floppy ears and a waggly tail.
You won't find much in the way of usable green space in the nearby vicinity. If you're an ocean fan, you may have to drive down to Cocoa Beach if you want to take your dog out walking along the sandy dunes.
As you might expect when living along the beach, you and your dog will have to get used to dealing with the traffic. During the day, this is a bustling stretch of road, but traffic gets quite heavy during the usual morning and evening rush hours. Unless your dog is used to walking along busy streets with lots of traffic noise, you should plan to cross Ridgewood Avenue and use the sidewalks in the nearby residential areas for your walks.
Once away from the main streets, you and your dog should be able to take long walks in the neighborhoods, most of which have sidewalks to utilize. Some of the areas even have shade trees that will give you both a break from the relentless Florida sun. The only other thing you must worry about in these areas besides light traffic will be wandering pedestrians. Use a short leash and they shouldn't keep you from getting out and about!
Since you can't use the beach that is less than a block from your home, you have no choice but to either rely on the few small public parks where dogs are permitted or to drive off in search of greener spaces.
If you are going to take your dog for a car ride, why not head straight down Ridgewood Avenue to I Dream of Jeannie Lane? Here, you will find a large parking lot and the Cocoa Beach Public Dog Park. The park offers a large fenced-in area for big dogs and a slightly smaller area for smaller breeds. Each area has plenty of room for your dog to run around with the rest of the pups, lots of shade, and water for your canine companion. There are public restrooms and beach access as well. Keep in mind that most areas in Cocoa Beach are open to dogs with certain restrictions!