At the southern end of the Calle del Cristo, just to the right of the Capilla, you'll find the Parque de las Palomas (The Pigeons Park). It's not very big, but it's super crowded - with pigeons, that is! Hundreds of pigeons hang around this little park and have built their nests in the small holes they have found in the fortifications' walls. Many people, especially those traveling with children, stop by to feed the birds - they're so used to having visitors, they'll literally eat out of your hand. Birds and I don't have such a great relationship (I've been pooped on more often than I care to discuss here) so I stuck to the part of the park that seemed a bit safer, but there was a lady getting her picture taken with a pigeon on her shoulder. To each their own, I guess!
Just like San Marco square, Parque de Palomas has many pigeons. Located right next to Capilla de Cristo with views of the caribbean this park is a nice spot.
The children love coming to this park and feeding the pigeons. Me, I love animals but pigeons are on the bottom of that love list. They carry so many diseases and caution should be the first priority. So, if you want to feed them, toss the food to the ground and watch them from afar.
Please Note: Do not allow the pigeons to climb all over you, it is a health hazard!!
Palque de las palomas was a great and fun place to visit. I say was because unfortunately it has closed. I was there with my son on June of 2012 and we found out it was closed due to health reasons. I found that weird as I was there in November of 2011. I checked for myself and it was true.
Old San Juan is surrounded by the old city walls. Go to the Parque de Las Palomas (Pigeon Park) to see part of the old wall and maybe a view of the port.