Here's a trick for you. You've got a large world that can be explored in a nonlinear fashion, and you don't want the player to have to walk that same stretch of ground over and over.
In Zelda 1, you always started the game on a certain screen in the overworld, or on the first screen of a dungeon in the underworld. This had the effect of making the overworld like a giant, "loose" level: when you were in death mountain area, you were a long ways from that first home screen and so you didn't want to die. This made sense because Zelda 1 had lots of enemies roaming the overworld, which got more difficult the further from "home" you went.
In the dungeons it made even more sense because they played out even more linearly: by the time you got to the final boss you had braved many dangers and wouldn't want to have to go back to the start.
*** Digression! ***
You remember how you'd always start out with three hearts? At the start of the game, you'd only have three hearts in total anyhow, so no big deal. However by the time you got to the middle section of the game, three hearts wasn't very much. The first thing you'd always do was walk to the fairy so you could get refilled. When you were tackling dungeons, you had much the same problem. You'd die, and warp to the start of the dungeon, but good luck tackling it with only three hearts! So you'd have to go to a nearby fairy spring. And maybe even buy healing potions, a lot of preparation!
Zelda 3: LTTP (the SNES one) fixed this dungeon-hearts issue by putting fairy springs in the dungeons themselves. A nice twist!
What's interesting to me is how similar this problem (situation? mechanic?) is to what we see in a shooter like gradius, where your weapons power up as you play. When you die you start back at the last checkpoint, but good luck making it last without your weapons. In some shooters this becomes a crippling problem for the player, so that the game almost operates in such a way that you have to play certain large sections without dying, or else you're stuck.
In the case of Zelda, it isn't so severe and so it's OK. I still think it's a little bit arduous, visiting fairies and collecting heal potions, but it has the upside of creating a higher level of anticipation for your dungeon-dive or boss-fight or whatnot. For shooters though, it's really a gameplay design bug similar to a game where you can save at such a place/etc. that you can't beat the game and have to start over from the start.
*** End Digression ***
In Texas, I need to prevent the player from walking overland too much because there isn't supposed to be any particular challenge to the overworld, at least most sections. So if you quit or die, where should you re-start?
I think there are sections of overworld that will play out like in Zelda 1. There is a bridge that you cross and on the other side are monsters. But for the peaceful areas, I think you should restart at whatever screen you last entered. Since there is no special challenge or obstacle in moving from area to area here, you should just start where you left off.
This is fairly easy to implement, which is a nice side-effect. So in most areas it will auto-save when you enter the area, but if you're north of the bridge or if you're in a dungeon/etc. it will save only at designated checkpoints.
There are some other design choices to make there but they probably aren't too hard!