How much of this game is going to be spent with me having to level grind just to survive in a dungeon?
At the start you can plow through the dungeons with minimal leveling.

Later on it gets rather ridiculous for the 'I'll just fight necessary battles so as not to over-level' player. You have to grind just to be high enough to run away from the monsters. I suppose if you fought those battles in the first place you wouldn't have to grind so much, but I'm not wasting time fighting them just to be slaughtered by a boss at the end (without being able to save first might I add)!

I'm not bashing this apect of the game though, in fact I am rather fond of it. In other FF games you don't get the chance to level up your characters without removing every bit of challenge from the game. Try experimenting with different parties, it may pique your interest in leveling.