I have never cruised out of San Juan but did the Destiny in Aug/Sep this past year over Labor Day week. It was a great cruise! I arrive eary but the airport wasn't a problem nor was only speaking English. Toured Old San Juan on my own.
Took a cab getting off the cruise ship and went right to the airport. It wasn't a problem, yes there were lines at times, but they moved. Waited for a couple of hours to board the plane home
( It wasn't bad. It was much better and easier to get through than Fort Lauderdale airport on my last cruise.
The only drawback to a cruise out of San Juan in my opinion is the airfare tends to be higher, but it is served by all the major airlines.