Near the sea coast these states share part of Brazil's Coastal Plain. Their interiors are in the Central Highlands. Short rivers drain to the sea in this areas' north. The south is bounded by the São Francisco River, whose tributaries drain much of Pernambuco.
In common with Brazil generally
The state capitals of Pernambuco and Alagoas, Recife and Maceió, have more than a million residents in their metropolitan areas. Recife, built on an island, a peninsula and the mainland proper, is know for its daily newspaper, published since 1825, and its Sugar Museum. Maceió is located two kilometers north of the Lagoon of Mundau, and is famed for nearby beaches.
All the pre-Columbian peoples spoke languages that Joseph Campbell collects together as Amerindian. Only one is still spoken, Fuluio, a Macro-Ge language. Many extinct unclassified languages and an extinct isolate were known to have been spoken here, as was a form of Tupi. I do not know if Tupi was spoken here before its spread as a colonial lingua franca.
(1) Officially Brasil since the late 19th century.
(2) Nordeste in Portuguese.