Q. What is it supposed to be on the show? A. a park, with a lighthouse. Q. Where is it supposed to be on the show? A. Somewhere in Miami. Q. When did we see it on the show? A. In Episode 1, of Season 8, "A Beautiful Day". At the very start of the new (final) season, we see Dexter out enjoying himself, happily helping Harrison fly a kite. This short scene is part of a beginning montage (along with the soccer game scene) showing Dexter enjoying life without LaGuerta. This is in contrast to his sister, Debra, who is slowly disintegrating as a result of the guilt she feels over killing LaGuerta. But Dexter doesn't really feel guilt, so he's just glad that the threat posed by LaGuerta is over.

A. A public park - with a lighthouse.

A. This scene was shot at Shoreline Aquatic Park, in Long Beach, CA.

It's the same place where they filmed the scene of LaGuerta's memorial service, and the later scene (at the end of the episode) with Vogel.

Shoreline Park is located on the south side of Rainbow Harbor, across the water from Shoreline Village, and just a short walk from the Aquarium of the Pacific.

You can't miss that white lighthouse, which officially goes by the (somewhat awkward) name of "The Lions Lighthouse for Sight".   (The Lions Club partially paid for erecting the lighthouse, highlighting their club's charitable efforts to prevent blindness.)

The lighthouse sits perched atop a grassy knoll at the east end of Shoreline park.

I'm sure this was meant to be a sunny, blue-sky scene, but since they shot it on the morning of February 19, the winter weather at the coast didn't cooperate.  So, they made the best of the overcast sky, and inserted a rainbow.