Lucky you! The interior of Puerto Rico is quite mountainous and there's some great hiking to be done. Be sure to check out El Yunque, a sprawling rainforest—the only one on U.S. soil—that's maintained by the Forest Service.
Fiding the right footwear for Puerto Rico is difficult because it's so hot and humid. You'll want boots that are protective, but also light, breathable, and fast-drying. And you mention you have some fit issues as well, although there are ways to deal with those.
The Vasque Breeze ($160) is a good starting point. The Breeze is a nice light-to-midweight hiker with leather and mesh uppers that stay breathable in warm weather, a Gore-Tex insert to keep your feet somewhat dry, and nicely lugged outsoles for grip in soft soil or mud. It's a great boot for day hikes or light backpacking trips.