My husband (who is from here), myself and our girls just moved here in January. At first I was a little nervous to go out on my own, but found that it is actually pretty safe if you just follow a few rules, like not bringing a purse with you, stay out of seedy areas where you see a lot of homeless people or junkies around (Their are a lot here), stay OUT of low-income housing areas, etc. My husband just mentioned to me, not to piss off the men riding horses, as they typically carry guns and will shoot. It is actually pretty safe here, so if you just use common sense, you'll be fine. Just be friendly to people and they will return the favor. 😊
The first time I visited here, it was in August and I loved it. The weather was great, actually, if only a bit humid. I suggest trying a fruit here, called Canepa. It comes in a bundle and they look like a small round key lime, and is not sold in any stores. You can buy them on the street out of the back of people's trucks for $3-5. The season for them is June-September, and they are amazingly good. You split them open with your teeth and pop the little peach colored ball into your mouth and suck on it like a candy, and once you suck down to the large pit, you just spit it out and pop in another. 😊
My husband suggests visiting the Boqueron beach, Rincon, Mayaguez (that's where we live and it's beautiful here), Also, if you visit the lobby of any higher-end hotel, they will have a free booklet of places to visit and activities to do, like the glow-in-the-dark lagoons and horseback riding on the beach, snorkeling, etc. Old San Juan is a must-see. It is one of the most beautiful places that I have seen here.
As for transportation, I would suggest renting a car if you can afford it. Public transportation in San Juan is pretty good, but everywhere else it is not.
For more information, I would visit this web site I just stumbled onto yesterday called, Robertospuertorico.com. It is also known as, The Scurvy Dog's Puerto Rican Blog. It has a lot of good information that you could definitely use.
I hope I helped a little and that you have a great time here!