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May want to look at

Have not used them but the rates sound reasonable. Maybe others can make better recommendations.
The airport is in Isla Verde the same as several of those.

There's a hotel right in the airport with relatively low rates that's used mostly by folks with either late arriving or early departing flights.  The convenience of this is that you won't need any transportation, and you will be within walking distance of the airport car rentals or shuttles to the off-airport car rental agencies the next day. 

The beds can't be beat at the Sheraton in OSJ.  Prices reasonable but not cheap.  They may have an airport shuttle.

just limin wrote:

There's a hotel right in the airport with relatively low rates that's used mostly by folks with either late arriving or early departing flights.  The convenience of this is that you won't need any transportation, and you will be within walking distance of the airport car rentals or shuttles to the off-airport car rental agencies the next day. 

We've stayed here several times before early AM flights.  Nothing fancy, but makes dealing with the airport super easy.

Is this your first time in San Juan? It is completely safe to take a taxi from the airport at that hour, and later. I say that because obviously it is not true everywhere! If you expect to be tired I'd just recommend you find a hotel in Isla Verde (there are many!) and take a cab there when you arrive. Cab fare should be less than $15. I would not recommend you stay in the airport hotel.

One that looks nice to me every time I pass it is the San Juan Water & Beach Club (~$130 on hotels.com), but, as I said, there are many options. I would avoid the super-budget ones such as the Villa Verde Inn or the Coqui Inn, which are on the other side of the highway, but that still leaves you with a ton of choices, and if you are coming soon (i.e., the summer) you should be able to find plenty of deals.

Thanks everyone. Yes, it will be my first time. I am a "planner" so I am researching everything in advance. I am no stranger to big cities and am not afraid to take a taxi. Hotels online vs how they appear in real life are different. This forum has been AWESOME (and patient) in answering all my questions (I know there has been a lot). My husband and I will be flying down in October-ish to find a place to rent. He speaks fluent Spanish (me, not so much), so he has been looking at rentals on the Classificados website.

I have used the hotel in the airport. It is good for one night. Then you can get a fresh start in the morning. 
Also, check the AirBnB website for rentals around Puerto Rico.