What time does the daily quest timer reset? I play on the US WildHammer realm, if that matters. Its a central time zone server.
It's generally 3 AM or 4 AM server time, based on whether Daylight Saving Time is in effect, but the exact time the server resets depends on the server: you can find out the exact time by logging into the game and hovering your cursor over the quest count in the top-left corner of the quest log.
... reset timers for recurring in-game activities such as daily/weekly quests and raid/dungeon lockouts will be updated to a single unified lockout time of 15:00:00 UTC (8 a.m. PDT / 1 a.m. AEST) for all North American, Latin American, and Oceanic realms. -- as of July 01, 2016.
The daily quest reset is set per server and never changes.
The exact reset hour depends on the realm, but it never changes, is chosen to be in the early morning, and will not coincide with the instance reset.