I would suggest a basic reputation system for all the important factions similar to Fallout New Vegas. I would also allow Kings to create their own missions and send groups of Adventures on different quests.
There are a few good random encounter tables for wildlife, interesting plants, odd landmarks, etc.
On any day of travel that has no encounters, or even if they do, roll a few of these and narrate.
The players may decide to hunt, forage or investigate and you can adjust their progress accordingly.
For example, my players often found mysteriously appearing or disappearing tracks (crossover to Fey realms), mushroom rings (some edible), or foundations of old ruins with nothing particular to explore.
Just like the miscellaneous dungeon dressing tables, dress up your wilderness. Maybe make notes of what you roll.
The players might decide to stash heavy loot somewhere and come back for it later. The <roll> black boulder by the <roll> hollow tree where the river turns east will be easy to remember.
Also, this is a great campaign for side quests, so any module or scene you've been wanting to try can fit somewhere. Those "empty" hexes are perfect.
A final thought. If you roll no encounters, try rolling twice. The party sees those two encounters dealing with each other. They can get involved or not. Like trolls catching pixies, or thylacines and wolves circling each other. It brings the world to life.
I added a "tree of life" growing at the intersection of two ley lines... made Old Bedlam, or whatever her name is, into a real Witch (ley line guardian archetype). Just for fun. No real mechanical purpose.
I had a three way war going on in the prairie between Mites, Goblins, and Kobolds... the party ended up choosing the side of the Kobolds and now the prairie is free of Mites and Goblins. And now there is a thriving Kobold community living in the gold mine.
Low level encounter with a roaming warparty of Gnolls and Pugwampi, because Pugwampi are fun.
Add a volcano.
An underground network of tunnels/caves with subterranean rivers.
A small pool of water that is bottomless and perfectly clear, it always reflects a starry night sky, regardless of the time of day or the weather.
A clearing in the forest which has a large ominous bloodstained rock in the center acting as a sundial.
An oasis that is completely backwards, everything is disproportionately sized, trees are tiny, flowers are huge, little bears, and big bees... all Alice in Wonderland style.
A dead, desolate hex completely devoid of life... it is a naturally occurring salt flat that can be mined/harvested to contribute to the economy during the kingdom building phase. Have it be extremely hostile to cross, such as the sun reflecting on the white surface is extremely bright and can cause temporary blindness. Or your water naturally dries out in this area. Your horses won't go into it without constant Handle Animal checks. If it's raining, the salty spray/fog that forms is mildly suffocating.
That reflecting pool is awesome. That could be great foreshadowing of chapter 6.
A couple pieces of advice:
You should browse through this forum's dedicated Kingmaker section. Lots of really cool ideas there, including unique hex descriptions, revised/expanded encounter tables, and other new content to add.
My advice is to not get too crazy with the exploration, actually. For many groups, the focus of the campaign becomes the PC's kingdom and the overarching story, and after a while, the exploration just becomes a distraction and/or it doesn't make sense for it to be a focus compared to the other things the PCs have to worry about. More specifically, my advice would be to add content to the blank hexes to start, but pay attention to when it becomes less fun for the PCs and then be ready to move on.