If you plan to stay in the San Juan area then you do not need a car as there are lots of cabs and buses which will take you almost every where. There is lots of traffic there since the roads are small and parking can be an issue so be prepared to pay to put it in a lot.
If you plan on visiting cities outside of San Juan then its a really good idea to rent a car. I rented a car from Charlie's car rental for $60 for the whole day which includes full insurance and it was well worth it. I got to drive around and visit the El Yunque rain forest at my own pace as oppose to relying on a tour bus's schedule. Also, driving through the luquillo area was nice and for the Bio Bay tour I had to go to Fajardo which is 45 mins away from San Juan so renting a car was definitely a plus. I was quoted $120 rountrip for cab ride from San Juan to Fajardo which was not just feasible since you can rent a car for the whole day for half that price.
Driving in PR is not as bad as people say it is but if you are use to NY driving then it wouldnt take you long to adjust there. People do drive carelessly so just have to use honk and pay more attention then usual. I only had one bad experience driving wise and that was when I was at a wallgreens parking lot out of all places. Some one backed into my rental car at 5mph and then casually just drove off. I honked and it was just too late, I guess they werent kidding when I heard drivers there are careless. I didnt go chase the guy down but instead got out of my car to look at the damage and saw only scratches and decided its just not worth it. Aside from that little incident, every thing else was smooth sailing and I would definitely rent a car to explore the rest of PR and especially places outside of San Juan.