Recife, with its quater Boa Viagem, is a nice beach with natural rocky pools (they protect you against shark attacks), nightlife, and restaurants. Olinda, an old 17th-century town near Recife, has fine examples of colonial architecture, including UNESCO's Patrimonio da Humanidade.
Southern beaches are the best. The top one is Porto de Galinhas with its natural pools. Another nice beach is located at Calhetas. Northern beaches are not recommended if you feel like swimming. Itamaraca, in fact, only has a Dutch fortress--Fort Orange--and a center for the protection of sea mammals.
Quick Tips:
We decided to stay in one of the beach-front hotels of Boa Viagem, and it was a good choice if, apart from visiting natural beaches, you want some nightlife. Beaches here are relatively clean--something you cannot say about Olinda's beach, which is very polluted. Olinda is nice for a one/half-day excursion, but not a place to stay. There is too much hasseling by locals who want to be your guide. Staying in Boa Viagem is the best in my opinion. You can reach Recife by plane--there are direct daily flights from Lisbon (TAP) and one weekly (Varig), or there are daily connections with domestic airports (Varig, Vasp, Tam etc.)
Best Way To Get Around:
We decided to go with excursions organized by local travel agencies. Our hotel was relatively cheap at R (less than US). The guide spoke only Portuguese, but you can easily comunicate with him in Spanish. Taxis are relatevly cheap as well--you can go to Olinda from Boa Viagem for about R (US return). Watch rate of exchange of Real. When we were in Brazil, currency was very weak--about R-5=US.