Olinda is the obvious one — Recife's UNESCO-listed colonial sister on the hill ten minutes north, with the cleaner streetscape and the louder carnival. Half a day is enough; a full day better.
Porto de Galinhas, an hour south by car, is a beach town built around a string of natural pools formed by an offshore reef — easily the best swimming in the region. Worth a long day or an overnight.
Caruaru, two hours west into the sertão, has the largest open-air market in the northeast every Saturday and the country's most important São João festival in late June. Itamaracá and Igarassu, an hour north, hold some of the oldest colonial churches in Brazil and quieter beaches.