I study in Honolulu. A few days ago, a tourist asked me "Do you live here?", so I answered "Yes." Then she said "What a life!" On hearing that, I thought it meant "what a great life!" because, you know, many think Hawaii is a great place to live, which is true. But the dictionary says it has the opposite meaning. What did she mean by saying that?
The comments from Jason and DrMoishe have this one right. "What a life" alone doesn't denote something as either good or bad; the context (especially her tone) is required to bring out the meaning that you're looking for.
"What an X!" is an exclamation meaning that X is extraordinary for its kind in some way. X might be extraordinary because of something good or because of something bad. You have to understand that from context.
What a dump! [Said when viewing a house, this means the house is a dump—a very bad house, almost as bad as a garbage dump.]
What a haircut! [Depending on whether your like the haircut or you dislike the haircut, this would have a positive or a negative meaning. The sentence draws attention to the fact that the haircut is extraordinary in some way.]
What a nice doggy! [Said when meeting someone's little dog, remarking that it's nice—that is, friendly.]
What a crabby old man! [This one is negative, remarking that the old man is extraordinarily crabby.]
What a generous old man! [And this one is positive, remarking that the old man is extraordinarily generous.]
As you can see, you can vary the phrase a little bit, like by adding an adjective before X. The well-known and much-loved song "What a Wonderful World" (1967, video with text here) clearly means "What an X!" in the positive sense.
There was a sitcom in the 1950s called I Married Joan, which had this line in its theme song:
What a girl, what a whirl, what a life!
The song is not well-known today, but it illustrates the ambiguity of "What an X!" The line means that Joan is an extraordinary woman ("what a girl!"), but it's because she causes a lot of chaos ("what a whirl!"). After those two exclamations, "what a life!" is playfully ambiguous, suggesting that a life with Joan could be good or bad depending on how you look at it, and it may appear good on some days and bad on other days, but either way you look at it, it is certainly extraordinary.