I was born and raised on the island but I haven’t lived there in many years. I still have family there and will be visiting this Summer. However, I would never, ever in a million years ride a bike anywhere in Puerto Rico. Like in most Latin American countries the rights of cyclists and pedestrians are the last thing on any driver’s mind. I think riding a bike is very dangerous there. However, I think running is fine as long as you know the areas to stay away from. If you are in mostly tourist or rural areas then running is ok. I would be careful running in inner city areas that you are unfamiliar about. And as for swimming there are a ton of beaches where you can go swim :-).
I would say Luquillo on the north-east side of the island (next to the Yunque rain forest) is one of the most swimmable beaches on the island. The beaches on the west of the island are better for surfing than for swimming.
Running in old San Juan (similar to the 70.3 course) is great but hilly. If was someone that was not familiar with the island I would stick to running in tourist areas close to resorts or in places like Old San Juan. And, sorry, I would not bike anywhere! BTW, Puerto Rico 70.3 has the dubious distinction of being the only Ironman event where a participant has been shot! It happened on the bike…