Not too far from the city center, the Teatro Municipal is one attraction to consider putting on your to-do list. Parque da Crianca and the Memorial da Resistencia are also nearby and worth a pit stop.
If you're looking for day-trip inspiration from Mossoro, you certainly aren't going to come up short! Aracati, just 45 miles away, has some great attractions which should keep you busy. Want an excuse to go check it out? Canoa Quebrada Beach and Nosso Senhor do Bonfim Church should do. If you need any more persuading, also consider Majorlandia Beach.