I spent a loooot of time in old San Juan. I'd like to think I know it somewhat well, but I could spend fifty more years there and still not find everything. Nonetheless, here is all I remember off the top of my head.
All the bricks in the roads are blue. The story I was told is that the Spaniards used them as lastre, the counterweight in sail ships. When they got there, they took them out, and filled all the weight on the ships with gold and took it back to Spain.
Only, there wasn't really any gold in Puerto Rico, and they probably dissasembled the ships when they landed for lumber.
El morro is the word for the fort built by the Spaniards. The turrets are called garitas. One of the garitas, el Garita del Diablo, is supposed to be haunted, but is closed to the public. I've been in them and can confirm all are deeply haunted, but only by the smell of urine.
There's a giant field where people fly kites in the wind from the ocean, and carts selling kites for those who didn't bring theirs. You can walk on the fort, no one will stop you, but it is a steep drop to the rocks and the ocean. tucked away near here, at the feet of the fort on the side of the ocean, there is a very crowded cemetary.
If you walk down a path near the wall, you find a ton of trees lined up, perfect giant climbing trees, along with benches.
Stray cats cover old San Juan. There is a rescue for the stray cats in one spot that does TNR. You can see the fruits of their labor in the clipped ears of roaming cats, and in the small shelters and food and water bowls that get more frequent the closer you are to the little house where they work from. There aren't usually stray dogs in old San Juan, that's more the rest of the island.
Pigeons are also absolutely everywhere. There is a place near el Morro called Parque de las Palomas, "Pigeon park", where they literally cover the ground. It looks like there are little holes in the side of the fort wall there for them to live, but I have no idea if that was the original intention for those holes. You can pay for food to feed them, and if you leave some on your arms they'll jump on to them and cover both your arms outstretched. Many of the pigeons are missing eyes, sometimes injured somehow or a bit sick seeming. They're all different colors too, which makes me think they might've come from domesticated stock, but I have no idea.
There are several statues. The two that I can remember are the one of Ponce De Leon (which got toppled in a protest a couple years ago and put back up by the city) and one of the lamb and the shield, which is the symbol of Old San Juan. Many revolutionaries don't like the shield because the lamb is submissive.
Piragua carts are always there.
There is a very old, very beautiful cathedral that you can just walk into and look at. It's called Catedral de San Juan Bautista. It's still in use, for services and weddings.
There's a little door painted to look like the flag. It's famous. Recently it was painted over in black and white. The black and white flag is used as a symbol of mourning, of a sign our country is in strife. It's used a lot by protestors.
The many candy colored buildings are sometimes people's houses, sometimes restaurants, sometimes stores.
Paseo de la Princessa is a walkway where all the artesanos (artisans) sell their wares.