How to parse and understand the sentence in bold?

Question

It's only 4 hours flying time from Sydney, but a world away.What better place to rest than a country where the only place people hurry is on the football field and things are done in "Fiji time"?

Answer 1

It's not, formally a complete sentence.

The idiom What ADJer NOUN than Y? is a colloquial abbreviation for What NOUN is ADJer than Y?

What more romantic place than Paris? = What place is more romantic than Paris?
What better man for the job than Chris? - What man is better for the job than Chris?

The idiom NOUN to VERB in this context means NOUN for VERBing.

Consequently, your example may be understood as

What place is better for resting than a country where
[a] the only place people hurry is on the football field and
[b] things are done in "Fiji time"?

Answer 2

This is a type of minor sentence. It's a rhetorical wh-question, and its structure is very simple:

wh-word + comparative

Since it's a rhetorical question, no answer is expected. Instead, the question is used to imply a superlative about the topic of discussion:

What [ better place to rest than a country where the only place people hurry is on the football field and things are done in "Fiji time" ] ?

Here, the rather long noun phrase is the topic, referring to Fiji. The implication is that there is no valid answer to the question, and therefore there is no better place to rest. As a result, this question is understood as a superlative statement about Fiji with the following meaning:

Fiji is the best place to rest (because it's a country where the only place people hurry is on the football field and things are done in "Fiji time").

Since it's a type of minor sentence, it doesn't fit any of the major sentence patterns you typically encounter.