the rainforest is actually very tourist friendly, they've made it that way. its about a 30-60min drive from downtown San Juan depending on traffic (which can be bad). as far as safety, generally speaking, if it seems sketchy it probably is. people dont really mind the whole camera deal and many people speak english also. the rainforest is also really camera friendly with many scenic lookout spots. go during the week if you can because it can get crowded on the weekends.
if you can make a day of it, i really really really suggest you drive down to the southwest corner of the island (bout a 3hr drive) to Cabo Rojo Lighthouse.. some spectacular beaches/cliffs and seafood!
plus you get the sunset on that side so.. if not, go to towards Arecibo, there are many old volcanic rock formations and rugged coastlines.
just avoid areas where you end up by yourself especially with gear. do you know someone there? i am puertorican and speak spanish so i blend in very well, but like anywhere else, drawing attention to yourself (and your gear) probably isnt a good idea.
its not an overly dangerous place to visit tho. its busy, bustling and lots of fun (crowded too lol), just use common sence, and take the advice of many of the posts on the sticky threads above!