What is your hope for the new year?

What is your hope about the new year?
What is your hope for a new year?
What is your hope about a new year?

(Which one is correct?)

The first one is best.

The first is by far the best. "The" is better than "a" since you have one particular year in mind. "For" is better than "about" when used with "hope".

All of the sentences you have provided are grammatically correct and convey the same general meaning. The choice between using "for" or "about" is a matter of personal preference and does not significantly affect the overall message. However, "for" is more commonly used when expressing hopes for a specific time period, such as the new year. So, in this context, "What is your hope for the new year?" or "What is your hope for a new year?" would be the more commonly used phrasings.