If you're planning a trip to the Island of Enchantment, you probably already know this, but it merits pointing out again. This makes it so easy for US citizens to travel there--no passport necessary, no worrying about money conversions when buying stuff, AND no worrying about going through customs on the way back! It also makes it easy for other travelers as well. I often call Puerto Rico "Latin America for beginners" because it has a lot of the perks of a Latin American country--awesome food, colorful culture, and friendly people--without some of the drawbacks, like worrying about whether it's safe to drink the water, whether you can flush the toilet paper, or whether you're two years of high school Spanish will be enough to get around (almost everyone we encountered was bilingual!).
We explored Old San Juan the first day, and despite the fact that I put on and re-applied sunscreen throughout the day, I still got pretty sunburnt (see the picture from the next day). If you're coming from somewhere in the continental US or Europe, the sun is likely going to be a lot stronger than you're used to in Puerto Rico. Bring water with you, reapply sunscreen often, and keep in mind that we found the sunscreen, aloe vera gel and other toiletries that we'd planned on buying there a bit overpriced, so consider taking that sort of stuff with you!
Puerto Rico is a super drive-able island. Pretty much everything is a two hour drive or less from Old San Juan, and you can see a ton of cool stuff on the island that's a bit off the usual tourist trail if you just get out and drive. For example, we had a rental car for three days of our stay and took day trips to El Yunque National Forest, Luquillo Beach, the Bio Bay in Fajardo, Cueva del Indio and the Observatory in Arecibo, Guanica Dry Forest, Tamarindo Beach, and Ponce, Puerto Rico. If you're staying more than a couple of days it's definitely worth it to rent a car! Be aware that, as in a lot of Latin American countries, the drivers are pretty aggressive so it pays to stay alert!
Keep this in mind when you're shopping, especially in Old San Juan. It seemed like the shopkeepers (or even workers at places like San Juan National Historic Site) were pretty reluctant to give change, and a lot of them wouldn't even take a $20 bill. We were staying at the Sheraton Old San Juan, so it was easier to change for some smaller bills at the casino there, but for an easier shopping experience change out your twenties for some smaller bills before heading out.
Old San Juan is a gorgeous area, with vibrant colonial architecture, historic forts, lots of plazas and sculptures, and gorgeous views of the ocean. We stayed in that area while in Puerto Rico, and definitely recommend doing that if you can. The area is also really easy to walk around. Get a map from your hotel and pretty much anything you'd want to visit will be labeled on it. You'll want to walk anyway, to better enjoy this unique place and because parking there is super expensive and a hassle!
Puerto Rico is in the Caribbean, which means that it has a dry season, a wet season, and that hurricanes can be a concern! Hurricane season runs June-November in Puerto Rico and those are the months when you can expect more rain as well. Not by coincidence, Puerto Rico's main tourist season is November through May. We were able to get a great deal on our flights and hotel through Expedia by going at the edge of hurricane season, in early June, and we avoided a lot of crowds that way as well. Not everyone will be comfortable doing this, but we were only rained on once the whole time we were there (see above). Just bring an umbrella, and enjoy the cheaper prices and thinner crowds!
Since we stayed in Old San Juan all week, it soon became obvious that whether a cruise ship is in harbor had a significant impact on the liveliness of Old San Juan. If there was one, there would be a lot more vendors selling things in the street, the horse-drawn carriages came out, and restaurants were a lot more crowded. We enjoyed it more on the days there weren't any cruise ships, as things were a mellower. It might be a good idea to try to find out the cruise schedule before going, or just keep in mind that if you're visiting on a cruise ship, it's going to be really busy!