Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Edinburgh to Eureka as you normally would.
Edinburgh Turnhouse (EDI) is the airport you will fly out of if you book a flight from Edinburgh to Eureka. You should not have trouble finding flights to Eureka from Turnhouse; the airport handles an average of 0 outbound flights to Eureka per day. You should also have plenty of airline options to choose from since 0 airlines have flights from the Edinburgh airport to Eureka. It is only a 6.8 mi journey to Turnhouse (EDI) from Edinburgh’s city center.