When flying from Kaua'i to Killeen, the time of day you decide to fly out makes little to no difference towards the overall price you’ll pay on tickets.
For a flight from Kaua'i to Killeen, you will be flying into Fort Hood Regional. Killeen Fort Hood Regional (GRK) is just 6.9 mi from the center of the city.
This is defined as Lihue Airport (LIH) and Killeen Fort Hood Regional Airport (GRK). Codes like Killeen Fort Hood Regional Airport are often used to just call airports uniquely.