Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Washington, D.C. to Napier as you normally would.
For a flight from Washington, D.C. to Napier, you will be flying into Hawkes Bay. Napier Hawkes Bay (NPE) is just 2.9 mi from the center of the city. Hawkes Bay is the only Napier airport and it handles 0 inbound flights from Washington, D.C. per day. 0 airlines have flights to Napier Hawkes Bay from Washington, D.C. on a regular basis.
While some choose either Washington, D.C. Reagan-National - Napier Hawkes Bay or Washington, D.C. Dulles Intl - Napier Hawkes Bay, Baltimore/Washington - Napier Hawkes Bay is the most popular route from Washington, D.C. to Napier.