I'm not quite sure I understand exactly what it is that worries you about sailing out of San Juan. We've done it many times and have never encountered any problems. The airport is fine, as are many of the hotels. In fact, there are many beautiful resorts and fine restaurants to choose from. While Puerto Rico is not our favorite destination (we usually visit only pre- or post-cruise), it is the largest, most developed and richest island in the Caribbean. Are there places that are unsafe for tourists to go? Of course, but then there are unsafe places in most cities in the world. Common sense rules.
If the Serenade of the Seas cruise is attractive to you and the price is right, go for it. I think you'll be pleasantly surprised by San Juan. As an aside, cruise ships usually leave the port of San Juan at night, which allows for a particularly picturesque view of the old city and lighthouse as the ship leaves the harbor.
Whatever your decision, enjoy your cruise!