Rainy season in Arequipa leaves but one option for the weekends: Beach. Within three to four hours, you can be out of the city and down at sea-level in Mollendo, Punta de Bombón, Camaná, or Mejia.
Each area is reachable by bus from Terminal Terrestre and colectivos also leave for Punta de Bombón from a parking lot near Makro. Tickets should be about 15 – 20 soles.
The coast gets really crowded on weekends but is still enjoyable. Table runners come down to the beach to offer you platters of ceviche, calamari, arroz con mariscos, and leche de tigre. The beach at Mollendo is right below a cute town with cheap sleeping options and good seafood; the beach at Punta de Bombón is a twenty minute walk or a 5-minute tuk-tuk ride from town. I can’t speak to Camaná or Mejia, though rumor has it there are great empanadas and slightly fewer people. If you can get there on a weekday, it should be absolutely beautiful!
Take a combi or taxi to Terminal Terrestre and look out for any bus company going where you want to go. Buy ticket and pay small tax at separate counter. Don’t forget sunscreen !