If you're playing Hearthstone excessively, you'll probably be able to plow through the daily quests without any problems at all - either by doing arena or simply playing one of your constructed decks. However, for the slightly more casual players, this isn't always as easy to come by - and it's quite "important" for your gold balance in Hearthstone to make sure you clear out the daily quests, at least by the time there's 3 of them, or there'll be "missed gold".
Now, I've decided to share my "mindless dailyquesting" strategy here, which usually gets the dailies sorted in a matter of minutes while I'm primarily focusing on ... well ... anything else to be honest! I've made mindless agrodecks, and switch the play to "casual" to avoid messing up my played rank, and just have fun seeing how disgusting I can be with primarily only spamming damage to my opponent's face.
Here's a sample of the basic decks I use, I've edited them slightly to attempt to only include basic cards, with a few rares sprinkled in here and there, and the odd epic. But, to be honest, you can replace them with basics and still do relatively well. You should note that this won't make friends, and (apart from the hunter deck) they probably won't do well trying to get high on the ladder, but they'll get the daily quests done usually quicker than "serious" decks would.
Now, the basic principle is really just to try to hit the hero for face damage as much as you can and don't trade minions unless your opponent has a huge damage potential with one of them. Everything should really be straightforward here, one note with the mage deck is to always save your frostbolts for when you have 1 or 2 ice lances for the bonus damage.