In my opinion, the quest system needs a complete revamp. Quests are unimaginative, boring, don't give enough interesting rewards and seem really random. They don't seem connected to the game world at all. Here are my thoughts on different parts of the system.

A) Quest huts.
I really like the progression of quest huts, from some small Inns to Witch Huts to Wizard Towers. Of course I wish there were even more of these different kinds of quest locations (Magical Groves, Feuding camps/villages..), but the current setup is already great.

B ) Quest level progression.
The higher level quests feel quite a bit the same as the lower level ones. It would be nice if high level quests actually were more demanding, more difficult (other than having higher level monsters) and more exciting. Some quest types that are missing that would be really cool would be:
    

1) Kill a certain NPC (that you don't control). Whether the NPC is neutral or owned by another player doesn't matter. You need to kill it to complete the quest - this might mean having to declare war on some kingdom or using diplomacy to make the other kingdom to give you the NPC on a silver platter. Wouldn't it be kind of cool to negotiate essentially the price on hanging of an NPC with your opponent? Would add a dimension to diplomacy, too.
    

2) Destroy a city / steal something from it. The truly high level quests should have really difficult dynamic tasks. Destroying a certain major / minor faction city would be difficult enough to make adventuring really interesting. Works the other way around - your city could be the target of an opponent's quets. In my opinion winning the game with a master quest should require you to do some very difficult tasks such as declaring war and raiding a village, or similar.

C) Quest plot lines.
Quest could have more continuity. Some level 1 quest could continue after entering a level 2 quest hut, eventually leading to top level quests that give big rewards. If all the quests are completely independent of each other, it'll never feel as grand as having longer quest arcs.

D) Quest prerequisites.
Currently, all you need to do is research higher quest levels to be able to do higher level quests. Here I think it would be good to incorporate something from RPGs, gateway quests. What I mean is having a level 1 quest that you have to complete before you have access to level 2 quests - this would be in addition to researching the required tech. Perhaps a quest you get from an Inn that gets you acquainted with the Witches of the world, thus allowing you to get quests from witch huts. Perhaps the quest techs should open up access to these gateway quests. Examples:
    •    Adventure tech name: Witch Lore / Witch Societies
    •    Flavor: During their studies in the dark arts, your researchers have discovered information about the Witch societies of <World Name>. Rumour has it these Witches occasionally hire adventurers for all sorts of exotic tasks. Perhaps you should spend some time in the Inns to get acquainted with these sorcerers?
    •    Opens up gateway quest that grants access to Witch Huts.
    •    Adventure tech name: Wizards' Trust
    •    Flavor: Finally, after years of maintaining good relationships, your loremasters have gained some respect from the powerful Wizards of <World Name>. The Wizards have also heard about your deeds around the world and are contemplating about forming a relationship with our kingdom. But first you must pass their test, which is administered by the Witches. Seek out Witch Huts to win the Wizards' trust.
    •    Opens up gateway quest that grants access to Wizard Towers.

F) Quest hut locations.
It would provide a much better immersion if quest hut locations were less random and more logical, like Witch Huts spawning in marshes, Inns along roads/at intersections and Wizard Towers in all sorts of remote locations (islands, middle of large forests etc).

G) Quest hut lifespan.
Another thing that would make the world seem more of a world instead of a grid of tiles would be to make the quest huts at least partially permanent, offering multiple quests each. A Wizard Tower wouldn't go anywhere once you complete the quest. Instead, after some 20 turns from completing the last quest it would have a new one. Every now and then a quest hut could vanish (inn go out of business/wizard tower crumble/witch hut burn), and soon a new one would spawn somewhere else. When a quest hut vanishes it would be really cool to have a goodie hut of the same level in its place, like "Tower Ruins" from a wizard tower.

H) Quest reward progression.
It would be great if you got more difficult and more rewarding quests after completing more quests of that level. So if you quest a lot you get better rewards than some lucky guy who happens to get a really good quest from the very first hut he enters. The Wizards you do quests for start to trust you and give you better tasks and better rewards.

I) Quest givers as NPCs.
One really exciting reward would be to for example to eventually get to control some powerful wizard that you completed a lot of quests for.

J) Additional quest hut ideas.
Other kinds of quets huts that could exist:
    •    Level 1: Inn (roads, close to cities), Refugee Camp (anywhere a bit more recluse than Inns)
    •    Level 2: Witch Hut (Marsh/Forest), Monastery (Plains/Hills)
    •    Level 3: Ruins (Anywhere), Thieves' Guilds (close to cities), Feuding Camps (of Humans/Trolls/Whatever, anywhere but quite rare)
    •    Level 4+: Wizard Tower (Island/edges of continent/other hard to reach places), Underworld (Mountain ranges, entrance spawns monsters often), Ancient Society (Island, rare quest hut which doesn't spawn at all in most games)

The higher the hut level, the lower the total number should exist in the world.