Diving in San Juan Puerto Rico is incredible. Warm, clear waters, and both the Atlantic and Caribbean seas offer unique sites. In San Juan, Puerto Rico, there are some dive sites, but the best dives are either on the west or east coast. For a more complete list of dive spots and a dive shop that can take you there, check out Aqua Adventures. The east coast, near Fajardo, is relatively sheltered and has many smaller islands within its area. The west coast is more savage and offers steep wall dives. For the more adventurous, the islands of Desecheo and Mona offer the best SCUBA diving.
Mona island is known as the Galapagos of the Caribbean. The entire island is protected. It is 50 miles from the mainland so it remains relatively untouched. It offers amazing diving with sea life everywhere. For this trip, you must have flexibility as there are no dive shops in Puerto Rico offering the trip, but there are some stateside dive boats that come down specifically for this. They will typically offer 4 nights to a week, with live-aboard accommodations. One outfit that does occasionally offer a trip to Mona Island is Juliet Sailing and Diving. For advanced SCUBA divers (ie NITROX certified), I highly recommend a trip to Mona Island.