Of course, a city of adventurers can't thrive without other facilities. Some, like the weapons or armour shops, are essential if you want your brave charges to be able to tackle more difficult quests. Others, like bakeries and parks, improve morale and keep your fighters fighting fit. As you move on, you'll find other buildings become essential to further progress.
White Mage and Black Mage Academies enable you to recruit the healers and sorcerers you'll need to defeat specific enemies. Gambling houses boost morale and help you recruit thieves, who are more proficient than regular adventurers in the gathering of loot. Without a Guild Hall you'll be unable to commission more adventurers or manage their pay. Build a tavern and you can organise adventurers into parties and use their combined powers to wipe out more dangerous foes.
We've had PC strategy games before, including Majesty, that have done this kind of thing from a remote, regal distance. I think that a big part of what makes My Life as a King work is that it operates on a smaller, more intimate level. The economics - basically maintaining a steady supply of gold and elementine - are fairly elementary, leaving you to be a fairly hands-on monarch. The more time you spend out on the streets, talking to the local population, the better you'll do in the game. Every person in town has a name and some kind of life going on, and their morale is raised just by talking to you.
Adventurers need care and attention. If there's trouble at home or they're too tired to battle, then there's no point letting them go on your latest behest - it's better to persuade them to rest instead. Meanwhile, your adventurers grow in experience and power as they fight monsters and complete behests, and you can also boost their skills by building and funding the academies that train them.
It's up to you to balance your missions so that your newer recruits have something manageable to build their skills, while your more experienced, hardcore scrappers go up against the major-league bosses. And if a minnow wants to go toe to toe with a beast that's beyond their ken, then you'll just have to tell them to go and gather experience instead.
A lot of this comes down to routine. Both the adventurers and the general population have routines, and working out how to get your adventurers most efficiently from home to bulletin board to city gate turns out to be crucial. By planning where you put the shops, academies and taverns you can stop them wasting half the day just navigating the city, and get them out there in the dungeons doing good. You too have a routine, starting the morning with reports and behests, then sending the adventurers off on their way. Then there's a little time for chat, management and building before your advisor comes to summon you to bed. And not in the way you might be hoping for, either. You're only a young king, after all!