The first place you should go is Acorn Park. This charmingly named little park is tucked away in a residential part of Franklin Park. This park has a full sized basketball court. It also has a small playground stocked with the basics. Your dog will prefer following Acorn Park's walking paths through the trees!
If you're looking for more action, Blueberry Hill Park is the largest recreation area in Franklin Park! There are basketball and tennis courts, several playgrounds with various equipment scattered through the park, and walking paths to bark about! Blueberry Hill Park is often busy, with peak hours being weekend mornings and weekday afternoons.
Franklin Park is a great base camp for exploring the whole area!