Papaya is all over the Hawaiian Islands. Unfortunately, finding some that is ripe and not on private property can be a bit difficult. Priced under $1 per pound at most fruit markets, it's probably easier to purchase the golden fruit when it's firm but slightly soft to the touch. Some people love limes in their papaya, some eat it plain. I love my papaya cold in halves with some vanilla yogurt.
Another treat to look for is green papaya salad. It is a nice alternative to try at the start of a meal out.