It really depends on what you want from your vacation, as well as your budget, obviously. Assuming money is not an issue, Old San Juan is very romantic and has a number of boutique hotels and fine restaurants (if you want something
very romantic,
very historic, and consider travel an entitlement rather than a luxury, then
El Convento is the place for you. In my opinion, it's the finest boutique hotel in the Caribbean outside of St. Barths, it's housed in a 17th-century convent, and it's not a chain hotel, so expect lots and lots and lots of luxury and charm). The Isla Verde part of town caters to younger, more hip tourists, with inventive beachfront boutique hotels and eclectic restaurants. Condado is more for folks who want something reasonably luxurious, but predictable and mainstream (with plenty of access to the beach).
As far as sightseeing, I really can't write a whole travel guide here (you really have to do your own research), but I can give you some pointers. Definitely devote at least a day to Old San Juan. See the two forts, the city walls, the Fortaleza, and just stroll through the city into the night. For day trips, consider El Caribe National Park on the northeastern part of the island. There are also snorkeling and scuba diving trips out of the nearby Fajardo, and that area is generally home to some of Puerto Rico's finest beaches. You can also visit Arecibo, southwest of San Juan, home to the world's largest radio-telescope and the SETI project. The city of Ponce, in the south, was cute in places, but driving there through the island's interior took such a long time, and Ponce itself is so crammed and difficult to navigate, that in my opinion it's more trouble than it's worth. The city of Mayaguez in the west is popular with surfers.
You might also want to consider trips to the islands of Vieques and Culebra. They are renowned for their natural beauty and wild life (and also give tourists a taste of a more rural, languid Caribbean). There are ferries operating out of Fajardo to both islands, as well as a local airline connecting San Juan with Vieques. Culebra is the more remote of the two islands. Definitely a good choice if you are an "off the beaten path" kind of traveler.