A few suggestions:
-- If price is no object (I mean, really) and you have the time (Rincon is about 3 hours from San Juan), Horned Dorset Primavera (http://www.horneddorset.com/home.html) is regarded as one of the most romatic hotels in the world! They'll be able to help you set up something nice.
-- With a little time, reserve a private dinner for two under a canopy on the beach at Villa Montaña in Isabela (about 2 hours from San Juan http://www.villamontana.com/index.html). I went there to celebrate my wedding anniversary last year and there was a couple with a table on the sand with torches and flowers... Very romantic! You can even stay the night, but the hotel is expensive...
-- If you don't have much time or money, reserve a table at the beach at Pamelas in Ocean Park (http://www.numero1guesthouse.com/pamelas.html). Plan it around for 6:30 so you get to be there for sunset. Request a table at the beach (they set them up in the sand).
-- Within Old San Juan, there are the big fortresses (San Cristóbal and El Morro) that lend themselves to concepts of strenght, timelessness, etc...
In any case, prepare for the hot and humid weather (rain is expected for next week) and have a plan B... Have a great time!
P.S. If you decide to go for a picnic at El Morro like Scorpionitty suggests, you can probably have your hotel prepare something nice. There's this place in Guaynabo (15 mins from San Juan) called Bottles (5 G Tabonuco St., San Patricio, Guaynabo (787) 775-1210) They can prepare something great and they have a huge selection of wines. Ask for Richard. Thay might even deliver...