In addition to an enormous array of hotels, inns, and guesthouses offering every kind of accommodation imaginable, San Juan [1] has a variety of daily, weekly, and monthly apartment rentals available to those seeking a homier or long-term place to stay.
El Viejo Adoquin (6 Calle de la Cruz, Old San Juan, 787/977-3287, reservations [at] stayinpr [dot] com, www.stayinpr.com [2]) offers several superbly located and decorated apartments in Old San Juan [3], as well as one in Rincón.
The Caleta Realty (151 Calle Clara Lair, 787/725-5347, fax 787/977-5642, reservations [at] thecaleta [dot] com, www.thecaleta.com [4]) also has many properties in Old San Juan and Condado.
Links:
[1] http://www.moon.com/destinations/puerto-rico/san-juan
[2] http://www.stayinpr.com
[3] http://www.moon.com/destinations/puerto-rico/san-juan/sights/old-san-juan
[4] http://www.thecaleta.com