If you are traveling solo and plan on just say visiting El Yunque as your only stop outside of San Juan, then you can do an organized tour
to get the most out of PR even for just a single day trip it is probly better to rent a car because...
The drive to El Yunque is straightforward and less than 45 mins from San Juan. You can stay in El Yunque for as long as you want and do as many of the trails as you ant (with organised toiur you are limited to what that tourm offers).
After El Yunque you could spend the afternoon at Luqillo Beach which is really nice and check out the food kisoks near the beach - very popular spot
If you had the car for more time, you could check out Guavate (south of San Juan) for the local roast pork (Lechon)
So really depends on what you want to see outside of San Juan