That’s an excellent question, but it requires a slight clarification about turtle behavior.
Sea turtles (primarily Green sea turtles and occasionally Hawksbills) in Kauai do not “sleep” on beaches in the way we might think. Adult sea turtles sleep while submerged in the ocean, often wedged under rocks or coral ledges in shallow nearshore waters.
However, what you are likely referring to is when turtles bask or rest on the sand. This is a behavior unique to Hawaiian green sea turtles (known as honu). They haul themselves out of the water to warm their bodies in the sun, digest food, and possibly to avoid predators. This is often mistaken for sleeping.
The most famous and reliable beach to see turtles basking on the sand in Kauai is: