Ok. Forget this “first glance”
Vitoria and Maceio don’t worth it. Although Maceio, as Recife is a way to visit some beautifuls beachs, but the cities are uninteresting.
Salvador, Natal and Fortaleza are a good choice, especially the last one. Once in Fortaleza you can go to Jericoacoara. Is the most incredible place I ever stay. And once in Natal or Recife you HAVE TO go to Fernando de Noronha, it’s a spectacular island where you can appreciate the wide life “in loco”.
From Salvador you can go to Itaparica (there’s a Club Med) or to Morro de São Paulo.
Once in Sao Luis go to Ilha de Marajó, with great historical center, as well, Olinda in Recife, and the neighborhood “Pelourinho” in Salvador.
There are too much to see in 4 weeks. So, if I were you, I wouldn’t spend time with big cities.
So, follows my tip:
Vitória - DON’T GO!
Salvador-Itaparica-Morro de São Paulo
Maceió - DON’T GO!
Recife - Olinda - Porto de Galinhas (2 days at least)
Natal - Praia da Pipa- Fernando de Noronha (3 days at least)
Fortaleza Jericoacoara (3 days at least)
Sao Luis - Ilha de Marajó (3 days at least)
Be aware that the roadway are very awful and sometimes dangerous. If you go by car, the indication along the way can make you lost your way. Unfortunately it is true
Last tip: The Brazilian language is Portuguese.
Hope to help. Have you a good trip!