Just one night or more?
I like staying in Old San Juan - lots of history, good food and sites to see - all in walking distance. OSJ is a very short taxi ride to the Pan American Port.
We just stayed at CasaBlanca in OSJ. Had a great room(s) for us (queen) and the adult kids (two twin beds). Two bedrooms with shared bathroom in between. We very well might be staying there again next January as well. Floors are NOT carpeted - tile / stone. We did wear our flip flops in the room - there did seem to be stuff on the floor. NO TV, but they have a tablet in the room with Netflix and other entertainment options. Down in the lobby they were showing ... wait for it ... Casablanca
Few years ago we stayed at the Sheraton, but reviews have been giving it only 2 stars - so it must be going somewhat downhill