DH and me stayed at the Sheraton Hotel & Casino by the convention center. We sailed on the Dream to PR and the terminal we disenbarked from was very close by, it is different than if you are stopping in San Juan. When stopping in San Juan you dock at the terminal in Old San Juan.
This hotel had great amenties, there was so much night within walking distance to this hotel. We stayed here for 3 nights after our cruise and explored PR a little.
It is close to old San Juan.
Good luck.