That is our plan for the same cruise. They should let you board around noon to 1PM on departure say. Board the ship, get yourself settled and then get off the ship for a tour of the old San Juan area (which is right there anyway) and then be back on the ship by 8PM or so... The ship does not leave San Juan until 10PM, you should have plenty of time to do that.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013