You should talk with your sponsor, but here are some areas to consider.
The base is in the town of Guynabo that is an option,
Around there you have Santurce, Bayamon, Sabana Seca, Levitown, Toa Baja.
Be warned that these areas around the base are highly populated, so you are dealing with traffic and higher crime than in PR in general. You may want to consider a gated community to live in as it affords a little better security.
Dorado is also close by but it is expensive for a military salary.
Caguas may be a stretch for driving.
Due to traffic and small roads / stop signs / traffic lights, etc to get to the major roads, you are looking at a minimum of 20 minutes to get to the base, more than likely around 35 minutes.
Check classifiacados for rentals and remember that you are likely renting just 4 walls, there may not be a stove or refrigerator. Get them used in that case, preferably gas (propane) stove to save on electricity. A fill of a gas tank for a tall bottle is around 100 and will last you 4-6 months, the same will be a lot more for electricity specially if you use an electric oven a lot.