Since i've been playing 13th Age i've noticed the emphasis of my prep time steer steadily away from mapping, and managing minutia (as 3.5 and 4e required) to focusing on broader strokes and modular elements that might appear in my campaign.
I've started to use a flow diagram for railroaded areas (such as dungeons) ensuring that each point (representing an encounter) has multiple places to enter/exit to/from and modular sheets with bullet points of info for more sandbox areas. (see here about "Jaquaying" your dungeon layout)
Im too worried about drawing a huge dungeon layout and spending time mapping each and every corridor (although i'll do it where it makes sense) - generally my players are bored of it and want to get straight to the action or story. We zoom out and roleplay the journey and zoom back in when the actions dictates. Remember the montage where indy travels across the world with the red lines shooting across the map? Kinda like that. But with dungeons.
Why does this work? I focus on the drama, cut off the fat and keep the juicy stuff. It works for my group, they aren't interested in micromanaging rations or the journey. Its about what happens when they get there and as long as they felt like they've travelled they're happy.