What's It Like?
Every single piece of the hexcrawl will be an attempt to answer this simple question: what is it like? Actually, every bit of the DM's job in every game is always to answer this question. Rather than get into another conversation about the nature of epistemology -- and I can feel a serious bout of neo-classical foundationalism coming on -- let me talk about this central question first, then move on to why I put this particular cart before any horses.
It is the goal of every writer, artist, game designer and DM to convey to a reader/perceiver/player/whatever what a particular experience is like. This is the basic structure of communication. In games specifically, DMs who merely expound upon what, say, a dungeon is without getting across what the dungeon is like are not really communicating, just explaining. The difference between "is" and "is like" is an experiential one: the former tells us objectively true (well, maybe not true; illusions are a thing) facts about the space in question whereas the former tells us about the experiential data of being in that space. Is it cold? Is it humid? Is there a bad smell? Does it remind me of anything? Stuff like that.
For the dynamic hexcrawl, it's important for the DM/GM/Judge/Referee/whatever to have an idea of what things are like. In a broad sense. A guiding aesthetic that can help you answer the questions that your players will ask that you're not anticipating. All in all, what will your sandbox be like? Everything else in your sandbox will flow from this one answer.
The Central Aesthetic
In preparing any sandbox -- whether it's the wilderness hexcrawl/dungeon environment of Hyperbarbaria or the Iron Coast or the urban pointcrawl environment of Ur-Hadad -- I spend some time developing a central concept of what the sandbox will be like. I wanted Hyperbarbaria to feel both familiar and alien to new and experienced players, so I took hints from both traditional sword & sorcery literature, drawing from the atmosphere of CA Smith, but gave it an unfamiliar edge by blending in many of the absurdist and identity themes found in WS Burroughs and David Lynch (lots of Twin Peaks shit, for sure!). While I've never really given the central aesthetic a name (or a naming phrase, if you prefer), there's a definite feeling that this confluence of dissonant donors creates in my head that I cling to as my guiding maxim for determining whether something is or is not Hyperbarbaria.
Similarly, for the Iron Coast, before I wrote anything (or even made Wizarddawn poop me out a hexmap), I asked myself what did I want the setting to feel like. The Iron Coast wanted to be more serious than Hyperbarbaria; it wanted to be a setting about the struggle of nations and warlords and armies against one another, steeped in mortality, bathed in blood. It wanted to be a setting where dungeons were not the casual stomping grounds of fortune-seekers but the impending tombs of the foolhardy. It wanted to be a place of mystery where the PCs have an idea of how much they don't know, how much has never been discovered, and need ask themselves whether mankind is better off knowing them. Big, bad, brutal.
Ur-Hadad can vary a bit depending on the group playing in it, but in general there are a few things that I want to be true each time folks experience it. I don't like "pseudo-medieval Europe" as the "default setting" for games. It's lazy, boring and ... well, I'll stop there before I say anything that gets me in trouble. In short, I don't like it. Personally, I'm more broadly influenced by central and eastern Europe than western (go figure), but when I decided to invent a city that was the jewel of its particular universe, the greatest of the great, the most ostentatious and opulent collection of humanity assembled in one place, there is no way my imagination will let itself be confined to one particular people or art style or religion or social structure or whatever you've got. Nope. I've got to have everything -- and nothing. Here, a huge point of the sandbox was that, since anything can happen, that, as has been attributed to Hassan I Sabbah, "Nothing is true, everything is permitted." I want a scintillating crucible of myriad humanities filled with every image and sound that I've ever come to associate with the species, that's then overfilled with new imaginings and wild prognostications. A huge inspiration (as I've mentioned before) is I, talo Calvino's Invisible Cities, especially revelation toward the end of the book that every city described is really the same city, looked at from so many different perspectives. That's my Ur-Hadad: never the same thing twice, but always the same in its difference.
Your Central Aesthetic
Don't write paragraphs like the ones I just did. Really, I didn't write paragraphs like them when I was coming up with those aesthetics. Don't let yourself be tied down to specific words about your aesthetic, because any words you might use are not expressions of what the aesthetic is like, but rather state what your aesthetic is. In game, it's no good to tell your players what the aesthetic is; instead, use the aesthetic as a guide to inform them about their experiences. At the same time, you will use the central aesthetic to inform your design process. When I'm designing for Hyperbarbaria, for example, I want to deliberately create dissonant or jarring experiences for the players, since that's a core part of the aesthetic. In the Iron Coast, I know that the design choices that I make need to lead toward the greatest possible brutality and the stickiest moral quandaries. In Ur-Hadad, I need to present the richest human tableau I can; if I repeat myself (unless it's recurring NPCs or locations), then I'm short-changing myself and my players. When in doubt, you'll go back to your central aesthetic and let it guide you.