We have had a lot more serious hexcrawling and sandbox management in Coup than in my experience before. Some tools that are in use:

Random encounters

Not a surprise. The default seems to be a d6 table with five common encounters, and on a six, rarer encounters, with double six giving a special (previously met NPC, slavers from the adventures of the same name, etc.) The tables are specific to regions defined in terms of environment and culture. At some point we had an encounter check (1/6) typically per hex entered or for time. An adventure typically has its own microbiome and random encounter table, which we then use.

Foresters (such as rangers) might, with a good tracking roll, learn what inhabits the random encounter table. Mid-level foresters (maybe 4+ or 3+) get to test twice and choose an encounter from those when in a familiar environment. High level rangers might be able to enter the random encounter table themselves, but we have not seen any such in play yet, so this is speculative. That is, we have not developed or extensively discussed the rules yet, so we do not know how they are going to look like.

Random encounters have delayed expeditions, caused at least one failed quest, and often just been things to ignore. There are spotting rules and reaction rolls, so sometimes everyone passes by each other and sometimes there is diplomacy, sometimes combat.

Hexcrawling

We use a couple of different hex sizes, one for glossed or safe or downtime travelling, one for hexcrawling proper. Tests to not get lost, maybe probabilities for finding food and water. 1/6 base chance of finding something interesting in a hex when entering, and extra chances if searching the hex. A dungeon entrance might be such an interesting feature. There is also 10 experience per hex or 100 per interesting hex, which is a pittance, since it is divided among the characters and second level is 1000 to 3000, doubled per level.

Terrain affects movement speed, whether finding water is a problem, what kind of encounters one finds, how easy it is to find a good shelter, how easy finding food would be, etc., as one expects.

Mule counting

A beginning party does not have much money, but should their succeed at an adventure (survive, bring back significant treasure) they might have 100 or a few gp per person. This takes care of most of their expenses and living costs (awfully high 1 gp/level/day; adventurers live like the millionaires they are), so adventures become a matter of resources; how many people should we hire, where are we going? We would typically equip parties of ten to twenty people and pay for hiring costs, provisions, equipment, maybe river boats, and so on. This causes mule counting sessions. We typically round quite heavily to keep it manageable, something I or whoever is taking care of the logistics can easily handle.

Not everyone enjoys the mule counting sessions, which is fine.

We suspect that a mid-level party with at least five characters of levels 3+ and some at 5+, no longer benefits that much from hirelings, who succumb to any fireball or similar awful magic. We are yet to see this. Maybe soon.

Carrying capacity

We use real weights to the accuracy any given player wants to. It is strictly voluntary to care. Several do. I do not bother for lightly equipped characters, but after my thief bought plate mail, I will figure out how much it weighs and so on when the game is otherwise slow.

Water is also heavy; food also weighs some. The weight of water is a limiting factor for long expeditions and arid terrain.

Weather

We have had a storm keep characters huddled in questionable shelter, suffering potential cold damage (but our cleric managed a protection from elements ritual circle), a tree almost falling on them (an open die roll determined that not that time), and psychological damage due to cramped conditions and so on, alleviated by performance and story telling skills. The game masters have some kind of weather generator table thing for Greyhawk, I think.

Season

We had the characters take a winter break, since many had struck rich and had money to spend. Season affects weather and has also affected river flow and thereby travelling speed. A character or two have also suffered minor injuries when rowing a bit much while unused to it.

There have been some long time processes, like lizardfolk eradicating some small settlements with 1/6 chance of the winter (was avoided), or a dryad in a cursed area becoming unseelie with a given chance of left to winter there (happened and we are dealing with her at the moment).

Disease

Monthly disease checks when we remember, with 1/20 chance per character; more if constitution is low or circumstances conductive to catching something, like the marshes we are now adventuring in. One important player character almost died of pneumonia when not letting their time-intensive task go, but made it to the end. (Such important dice rolls are obviously rolled in the open with open stakes.)

Rumours and adventures

Adventure locations (dungeons often) are placed on the map. There are a finite amount with rumours pointing to them, more low level ones than high level ones, and probably a bunch that are forgotten but that could be found by random chance and hexcrawling. We are running low on adventure locations in the starting operational theater of Selintan valley. To go for the scraps, follow the doubtless deadly higher level things, or move elsewhere? Or maybe we should actually use money on researching more adventuring possibilities.

Adventure sites have attracted other groups and there have been victories over and losses to them, including long-time rivalries.