One of the main draws of Fortaleza, beside its beach culture, is the amount of effort that has been put into reviving the region's history, particularly the downtown, which runs from Iracema to its two main squares, Praça José de Alencar and Praça do Ferreira. Sadly, there isn't a wide range of quality architecture or high-end museums, so the majority of the sight-seeing that you'll be doing will be within walking distance. Such a thing can often be a blessing in disguise.
The neighborhood any traveler wants to find themselves in, whether the preference is culture or food or nightlife is the Dragão do Mar. The colorful colonial buildings and the essential Center of Art and Culture can be found here, while about a mile to the southwest are the aforementioned public squares. Praça José de Alencar is where you'll catch the best street performers and is also home to the city's most recognizable landmark, the Theatro José de Alencar, while Praca do Ferreira (a few blocks to the east) is the main city square and is a fine spot for people-watching.
With that being said, there isn't much else in Fortaleza to build an itinerary around if you're looking for cultural immersion. If interested and in possession of at least rudimentary Portuguese, we suggest taking one of the tours that run every Saturday at the Banco do Nordeste on Rua Floriano Peixoto 941 in Centro. Check the website here.