Beaches
Fortaleza is a city of beaches. You can swim, enjoy the sunshine, relax, drink coconut water, caipirinhas, eat fresh fish, surf, kite surf, or ride a jangada.
Scroll through this photo page to get some impressions and ideas. I'm writing a bit more about some of them below.
City
There are several beaches right in the city.
East

East of Fortaleza are several nice beaches. Also, you can enjoy food on the beach, and see (or ride) the jangadas (sail boats).
One of them is Morro Branco, which has red sand dunes to explore. According to TripAdvisor, it's the #1 rated attraction in Fortaleza!
Praia Aquas Belas gets awesome reviews, too.
Canoa Quebrada is another one that is very famous. I've never been and would like to go. Here are some photos I found.
Prainha is rustic fishermen's village where you can find from busy restaurants with fun music and food on the beach where you can buy handmade everything to deserted kilometros of beaches.
Also have a look at this list of beaches to see what you like.
Be careful: many traffic cameras on the highway to there!
West

Praia de Cumbuco is also very nice. There are many sand dunes, you can ride a jumento (donkey), do skibunda (buttski), a sled on the sand dunes, and ride a buggy.
Paracuru is a beach town with some attractions and close to many of the most beaultiful beaches around there.
Lagoinha is considered one of the most beautiful beaches in Brazil (and one of Laurinha's favorites).
Jericoacoara is a hippie (now touristic) village built on the sand. And is one of the favorite points for kite and wind surf. By 4x4 is the only way to get there, or in a off road truck bus. Jeri offers many activities, buggy trips to visit lagoons where you lay on a hammock, drink a caipirinha, and eat fresh fish, hippie festivals, and dance some forró (local state music).
Camocim is some km after Jeri and has its same style without the tourists. You can cross rivers on a balsa (boat where you put your car), practice some kite surfing, and stop on remote frishermen's villages to eat fresh fish, crabs and shrimps, and drink fresh coconut water. Laurinha has friends there and is able to have a really local experience. We did that in 2014 and it was amazing.