What time does the daily quest timer reset?

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.

Per Blizzard:

... 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.

source: http://us.battle.net/forums/en/wow/topic/20745655899