The places closest to the port are pretty spendy (in my opinion). Anything with an address of 'Old San Juan' is close, if the address is 'San Juan' it could be a little farther away. I've stayed at Hotel Miramar and have it booked again for Dec. Reasonably priced ($118 includes taxes) and an awesome rooftop patio. There's some great restaurants within walking distance and in the morning I just take a cab to the port. There is no pool but the rooms are clean with fridge and microwave, also I don't get in until 7:30pm so really will just be eating, sleeping, then to the port after check-out the next day. Also I'm only 1 person so I hate spending $200 a night on a hotel room!
but not sure where those places are in reference to the actual port.
use Google maps, the whole San Juan area is not that big and you should be able to see exactly where each hotel is.
"Life has no limitations, except the ones you make."