Might as well outline my own idea. It comes from the perspective of playing a lot of games in the series and considering what elements I found engaging in each one.
1. Constant menace.
What I mean here is that everywhere I go in the overworld, something should be trying to kill me. Remember when the Stalkids popped up for the first time in OoT and started chasing you? Something like that. I want towns and villages to be safe havens, and even those should have little dangers. When I'm in the Overworld, though? Fight or flight better be the whole thing: enemies are dangerous, and there will be cases where some people will choose to flee. The world should be out to get me, and the only answer is to kick its ass.
Imagine if there was a tract of land dangerous enough that there's no reasonable way for a moderately skilled player to get past it early in the game, but they have to in norder to progress at some point. Imagine that in order to safely progress, they need to activate an item or an ability or wait for an event that makes the enemies temporarily non-threatening, but it's bound to run out - and it always runs out before you can make it, so the last leg of the journey is guaranteed to be a mad dash away from creatures that could kill you in two hits and very seriously want to murder you. I like the idea of menace translating into tension.
My addtion: Not every enemy should be generic (just increasing in speed and life). What I mean is, if the same "combos" (I know Zelda doesn't have them, bare with me) and/or moves allow me to kill every enemy so that my attacks are all the same, they are not interesting. The same is true for avoiding getting hit, if every enemy is identical to dodge (like tapping the dodge button at the last minute Ninja Gaiden 3D style) then they are boring. I want to have to use different tactics and methods against different enemies. (Zelda's have done this in the past, I want a lot of emphasis on it.)
2. Labyrinthean but coherent landscape.
I want it to take srious work to get from one end of the map to the other, or at least take knowledge of how the land is laid out. Instead of being long stretches of open plains (which are fun to ride over, I grant) there should be geographical obstacles everywhere that needed to be surmounted. More, I want to be able to fight my way into territory that I'm in no way prepared to take on. If I have three hearts and am fighting enemies who do two hearts per hit? Awesome. If I fight my way through this territory and find myself in a place where I can't advance because I lack the necessary item or skill? Even better. If I die on the way back, I restart outside of the area anyway, so no problem.
And when I say "coherent"? I mean I want to climb Death Mountain, turn around, and be able to pick out landmarks at a distance. I want to be able to look anywhere and say "How do I get there?" and eventually there is an answer. I kind of had this feeling in Ocarina of Time, looking up at Death Mountain: seeing a place before you can go to it is mighty enticing. OMG Yes!
3. Seeing what I'm up against right off the bat.
Now "seeing" and "knowing" are really different. Remember when Skullkid was the second character you saw in Majora's Mask? Or when Aganhim appeared in the boot-up cutscene for Link to the Past? Or Ganondorf was shown wreathed in fire before you walked into the Deku Tree? You don't have to know exactly what the nature of the threat is, but I like having a face to fixate on as my antagonist.
4. Enemy/Weapon synergy.
Now I don't mean that some enemies take certain weapons to defeat - that's okay for some enemies, but it shouldn't be the norm. Most should be completely killable with nothing but the sword. But I want items to be useful on some enemies.
See this?
This is the best item in Zelda history, and when they're making items in this ideal Zelda they should look at this. In fact, this is my point of reference. This item can smash obstacles, allowing level and puzzle progression. It can be dodged by limber enemies, making it useless on small quick things, but the damage it does would be tremendous enough to bowl over medium-sized enemies and be much more efficient than your sword on large, lumbering creatures. If you see something bad-ass enough to slap this aside, you should be crapping your pants in terror. I want that kind of logic applied to every single item in the game when it comes to combat.
5. Increased focus on surviving bosses.
Almost every boss in modern Zelda games is primarily about figuring out how to kill them. That's fine. It's one of the best parts, and is why battles are often so fun. But I agree with the old-timers when they say that they wish bosses were harder, and boss fights felt more like fights; few modern Zelda bosses get this as well as they should. So every boss fight should retain the element of "how the Hell do I kill this thing" that they currently have, while adding an "AGH HOW AM I SUPPOSED TO DODGE THIS THING".
Helmasaur King is kind of the golden ideal as far as this goes. Or LttP Ganon.
6. Active Story-Telling (tm).
This doesn't mean more cutscenes - cutscenes are fine and dandy, but they're not exactly what I want. What I want is to have to actively initiate the fleshing out of the world around me, like with Gossip Stones or sidequests in Majora's Mask or even the Scan Visor in Metroid Primie. The world takes on a much more serious, more immediate sense of life when I have ot learn about it through effort, and this also alleviates the problem some people have with having lore shoved down their throats.
I love lore. But I also like having to search it out.
7. Scenario built around mechanics, and music built around scenario.
The games so far are pretty good about this, but I want to reiterate the point for the sake of doing it. Take a gameplay concept, build a scenario around that, then music around the scenario. Anything that begins with "Link can turn into a Goron, a Zora, or a Deku Sprout" and ends up with this:
Is a good process. I love Zelda music, and building it around the scenario makes things incredible. I would not presume to say what they sould do with either the scenario or the music; I enjoy both enough that I trust whatever they would come up wit. Except this:
8. Let Aonuma build the scenario, without any restrictions.
He doesn't have to be the director. He doesn't have to be the writer. I do want him to make the scenario (based around the mechanics) because I like his scenarios a lot, particularly Majora's Mask. If Majora's Mask is him at his least constrained, then he needs to have his shackles off all the time.
9. If the scenario includes Ganon, play on his classic strengths.
Twilight Princess and Wind Waker had the best characterizations of Ganon in different ways, but Twilight Princess in particular missed out on what is perhaps the biggest source of menace in any Ganon fight from 1998 or before (plus Puppet Ganon):
Ganon is at his most terrifying when you can't see him clearly. Ganondorf works best as a visual threat who's imposing in his physicality, but Ganon is lent menace by not having a precise idea of what he looks like. His invisibility in the first game; his partial invisibility in Link to the Past; the fact that you basically fight him in the dark in Ocarina of Time, so you can only see the glow of his eyes and the gleam of his swords and the vague suggestion of bulk stading out against the shadows.
Ganon should be a creature of terror, and this is aided by the principle of being more afraid of things you can't clearly see. This principle isn't subverted by modern graphics, either: those only serve to enhance the effect.
I guess that's really all I have. None of these are necessary, and I want it understood that no Zelda game is like what I describe but they are still the best games in the world; this is just a melting pot of some of my favorite elements combined with all the elements I find most exciting.
This
10. A huge variety in environments that isn't limited to temples.
I want the travelling itself to feel epic. All the places shouldn't be too close together. Some of the best fantasy stories (Hercules, Odysseus, Lord of the Rings, Wheel of Time) involve going a great distance from home. I may start in the forest with the other "elves" but I want to save the world. Going through icy places, American Great plains style, desserts, tundra, mountains. Allow me to truly see the whole world and keep it varied.
11. Variety of major "dungeon" types
Not everything needs to be a temple. I do like Zelda's focus on what D&D calls "site adventures" but I want more than temples. I know that a Zelda "temple" can have any environment, but I like the idea of exploring ruins, mines, strange supernatural environments and the like. Again, it's been done before, let's see more of it.
12. Every dungeon needs lore
Basically a subtype of 6 above. I don't want dungeons to just be finding items and defeating bosses. I want to learn the places history. Who built it and why? Why are the monsters there? Are the monsters here opportunists or are they working for the "big bad". Metroid Prime 3 did this amazingly well, with every place feeling like it had purpose. Each dungeon should almost be like an episode of an adventure serial, having it's own story as well as being part of the overall narrative.