Once you're downtown, you can do a full historical tour on foot (see the map). The old city in João Pessoa is mostly composed by baroque and colonial architecture. You can start at Solon de Lucena Park and check the following sightseeing points:
These sightseeing points are very close to each other, but if you're willing to get in every building and take pics, reserve a full day for it, with stops to eat and drink. Some of them are huge. That's all downtown, there are shops, restaurants and snack bars all around.
In the metropolitan area, you can visit the Fortress of Santa Catarina, in Cabedelo.