The Sheraton Old San Juan is right across from the cruiseport, so that is convenient for precruise. You can walk to Old San Juan, which would be interesting. There is a lot of shopping (are they girls or boys? Thirteen year old girls might like the shopping.) Also, there is a historic fort to tour.
However, for most 13 year olds, I suspect the beach would be their focus. The Hampton Inn, in Isla Verde, is almost across the street, and just a short walk from the very lovely Ritz Carlton with a beautiful beach, and beaches are all public (though the loungchairs are not). Also, there is a very nice, reasonable casual outdoor restaurant there at the Ritz Carlton right near their pool and beach.
Another point: the Hampton provides a free breakfast, which is a nice bonus when traveling with kids. It is a very short, 5 minute cab ride from the airport, and then, as I recall, about a $20 or $25 cab ride from the cruiseport.
Hope this helps.