Hanaichi
It might look like a hole-in-the-wall, but this small Japanese restaurant has some of Cancún's best sushi. Expect sashimi, nigiri, and every type of roll imaginable; house specialties include the Copán roll (deep-fried shrimp wrapped in cucumber) and the Cancún roll (stuffed with eel and scallops). There is a sushi bar on the ground floor and an intimate dining area with a few tables upstairs. Granted, you may not hear crashing waves, but you'll have an authentic Japanese experience for a fraction of what you might pay down the road. Note that the sushi menu is in Spanish and Japanese, but not English.