Hello, Yess.
In my opinion, la Universidad Interamericana de PR (a.k.a. "la inter") is the all-round best university in PR. (http://inter.edu/i/). It is a private university and has a good course selection. It has multiple campuses, with the "main" campus in the charming but relatively isolated town of San German, on the southwest of the island, but also with a major campus in Guaynabo, in the San Juan metropolitan area.
There is also the private Universidad de Sagrado Corazon. (http://www.sagrado.edu/). I am friends with the Dean of Humanities here so let me know if you would like me to put you in touch with him. There is also the private Universidad Metropolitana (a.k.a. "la UMET") with its main (and only?) campus in Cupey, in the north of the San Juan metropolitan area. (http://www.suagm.edu/umet/).
I would definitely avoid the main public university UPR, as basically every semester at exam time protests/riots such down the university and students are unable to sit for their exams, making graduating on time nearly impossible, not to mention all of the doubt and frustration involved. Also, UPR is perennially at risk of loosing its certification because the place has become mostly a joke. It's a shame to say this about what was once such a fine institution but any student who has the money opts to avoid UPR. (It reminds me a little of the Universidad de Panama when I lived in Panama, although I would say the constant disruptions of class and shut-downs of the entire campus are worse at UPR than they were at UP.)
There is one exception to the above rule and that is if you wish to study engineering, which I believe UPR has the best (or is it only?) engineering program, which is taught in Mayaguez, on the west coast of the island. Also, if you wish to study a non-typical foreign language, like Chinese or Italian, I think the main campus of UPR in Rio Piedras (San Juan) is the only place that would offer any courses.
I am not sure what you have to do with foreign transcripts. Perhaps the websites cited above will give you guidance.
All of that said, if you are moving to PR just for the education (beyond the obvious familial ties you have there through your father) or to have a career, I would agree with your Puerto Rican relatives and say you should stay away. You can get a much better (or at least, credible) education in the States and career prospects for anyone in PR are extremely dim if not outright extinguished before they even begin.
The crime situation depends largely on where you decide to live. Unfortunately, the drug trade has brought a lot of murder and mayhem to once-safe country towns. That said, San German is a very low crime area. Mayaguez? Not great. The San Juan metropolitan area, where Federal witnesses are assassinated in broad daylight on the major highways and murderers and rapists are rarely caught, is horrible for crime no matter where you live because it happens anywhere outside your home, in the nice places as well as the bad (although Old San Juan is relatively safe from violent crime except for the odd stray bullet that gets fired from La Perla.
Some people seem to think that because so much of PR looks relatively nice compared to other Latin American countries that the crime cannot be that bad. That assumption is mistaken. I have seem tin-roofed shanty towns built on mud in Latin America that have lower murder rates than run-of-the-mill neighborhoods in PR.
For the SJ metro area, I'd recommend Old San Juan (despite its frequent water disruptions), Condado (almost exclusively condos), maybe Isla Verde (mostly condos), Ocean Park (mostly houses), maybe Cupey, or if you don't mind marathon-commuting, somewhere farther up into the mountains like Caguas (a real city) or Naranjito (a small town).
Feel free to contract me if you have any more questions. Good luck!