When most people think "fantasy kingdom / domain", they think nobility, with a warrior elite supported by farming peasants. Here I'm running with High Medieval-style heavy cavalry nobles, but I'll leave enough of the math in to make it easy to switch it to old-school horse-archer samurai, berserkers, or whatever.
Executive summary: Every ten families under Feudal administration provide 60gp/season in taxes, 30gp/season in labor and materials for construction, and labor to maintain up to 1000gp in fortifications or roads. Additionally, every ten families provides the services of a knight (2nd-level elite heavy cavalryman), his squire (1st-level veteran heavy cavalryman), and two men-at-arms (heavy infantry) for one season per year (typically summer). All of their expenses (wages, supply, armorers) are paid by the hamlet for those three months per year. For every knight or squire lost on campaign, two families move from the Feudal estate to the Border estate at the end of the campaign season.
Feudal heavy cavalry (mixed units of knights and squires) have the following Domains at War stats:
3/6/9 Formed Mounted, AC 6, Unit HD 1+2, UHP 12, Morale +3, 3 lance and shield 9+, charge 3 hooves 8+.
So you have three numbers to keep track of: number of families (changes rarely), total fortification value controlled by nobles (increases slowly over time; feel free to track it in actual fortresses with floorplans, or not), and estate loyalty. I'm still thinking about how I want to handle estate loyalty; I think a common set of modifiers based on representation in the council of oligarchs, population change, strength relative to other factions, and unreasonable demands from the oligarchs should cover most of the cases, but I haven't worked them out yet.
Likewise, I'm not sure how I want to do random events yet. I liked 1e Oriental Adventures' approach, with a yearly "big event" and monthly small events related to it, but that's a lot of work to build. A more reasonable approach might be to build a table of templates, like Crawford's mad-libs.
In terms of seasonal random events, nobles like to fight, feast, and build castles. So some ideas there would be feud between noble families, hold tournament, raiding across the border, knight slays dragon and appears as nth-level NPC for hire as henchman, PC receives marriage offer from major noble family, and so forth. A drought, poor harvest, or widespread feuding could weaken the nobility. A weak nobility (below a certain percentage of total realm population) might lead to random events with bandits or monsters encroaching on the countryside. A disloyal nobility might raise an army against the oligarchy, hold a feast and slaughter any of the PCs or their henchmen in attendance, or have an NPC noble leader challenge its current oligarch for leadership (by single combat, of course).
Strategic locations relevant to the nobility might include areas of particularly fertile farmland (bonus taxes or natural population growth), particularly fortifiable locations like mountaintops and peninsulas (which boost the effective gold piece value of fortresses built on them and make it harder to besiege them), and locations which can restrict troop movement like river-fords.
Assuming average land, a family of peasants in ACKS produces 12gp/mo in goods and services and spends ~2.5gp/mo in festivals and tithes, leaving us with a pre-tax pre-garrison surplus of about 9.5gp/mo/family. We also know, from the Demographics of Heroism, that for every 50 people (ten families), there is one 2nd-level character, and for every 20 people (four families), there is a first-level character. So we're going to take a ten-family hamlet as our basic unit of organization here - it can support a 2nd-level knight, a 1st-level squire, and probably a 1st-level priest, wise woman, hedge wizard, or retired veteran mercenary, who we're not going to worry about.
A ten-family hamlet has an annual surplus of 9.5gp/family/mo * 12 months * 10 families = 1140gp.
A 2nd-level knight costs 115.5 gp/mo (60 in heavy cav wages, 38 in 2nd-level veteran wages, 1.5 in specialist wages, and 16 in supplies), while his 1st-level squire costs 99.5gp/mo (60 in heavy cav wages, 12 in 1st-level veteran wages, 1.5 in specialist, and 16 in supplies), so the pair of them together is 215gp/mo. Obviously, this hamlet cannot afford to keep them in the field year-round (that would be 2580gp, more than twice its annual surplus). Instead, they owe the state three months per year of service, typically exercised during the summer campaign season, consuming 645gp/year of the hamlet's surplus. Additionally, when called to arms, they bring two heavy infantrymen with them for an additional 72gp, bringing our remaining annual surplus to 423gp. The expenditures to support these guys more than covers the hamlet's garrison requirements (at 3gp/family/mo, 360 gp/year), and they spend the part of the year during which they are not serving the state at the hamlet, where they can take care of trouble as it arises.
Thus, in wartime, 150 families of peasants under noble / feudal rule can raise two platoons of feudal heavy cavalry (a mixed unit of 1st and 2nd-level fighters) and a platoon of heavy infantry. Feudal heavy cavalry, as a mixed unit of 1st and 2nd-level fighters, has 12UHP (twice that of mercenary heavy cavalry), and makes 3 lance attacks at 9+. It is otherwise identical to mercenary veteran heavy cavalry. 150 families is a decent borderlands six-mile hex; a population-dense civilized hex of 600 families would be able to raise two companies of cavalry.
ACKS notes that a reasonable tax rate is 2gp/family/month (60 gp/hamlet/season), which would consume an additional 240gp of the surplus and deliver it to the oligarchy's coffers, leaving a remaining annual surplus of 183 gp.
If this were used for fortress construction and upkeep, it would come to about 1.5gp/family/month. We could use this is a simple construction rate, where each hamlet yields 18gp/mo of free construction. This is... not very much, though, at 44gp/hamlet/season. Still, it adds up with many hamlets. If we take that 44gp/season and split it into 30gp/season of construction and 14gp/season of maintenance, then each hamlet can maintain about 1000gp worth of fortifications. This works OK with ACKS' assumptions about how big a fortification you need to hold enough land to protect so many families (in the borderlands case, 22500gp of fortress protects 25 hamlets, they maintain it, and also produce another 750gp/season in unmaintained defensive fieldworks on the eve of battle). You could try to balance between construction and maintenance automatically, but I've looked at the math and you end up with a differential equation analogous to the charging of a capacitor. Neat, but not worth the hassle for a game. Where does the extra construction go if it's not spent? The peasants put up new barns, redo their roofs, whatever. They are obligated to provide 30gp/hamlet/season in construction and 14gp/hamlet/season in fortress maintenance to the oligarchy, and if the oligarchy doesn't exercise those obligations, they go to waste. This is the nature of the social contract.