The only problem with cruising out of San Juan is the airport. It is poorly designed and on SUNDAYS it is unbelievably overcrowded. There is NO seating available until you have been through the security check-in. It will take you from 2-3 hours to get to a departure lounge where there is seating available. Therefore if you can delay your departure until Monday - do so. SInce you are planning to cruise in the summer, the situation may not be quite as bad in that lines may not be as long as in the winter.
Other than the airport, I cannot think of any reason not to cruise out of San Juan.