In your campaign, shouldn't your PCs be at least as busy as you are in real life?
Your group of characters is a band of heroes operating at least a little outside of the system to fix things that can't be handled well within the system. "We've got to do something about the kobold raiders now since the army is still a week away!" And once the word gets out about the new adventuring group, everyone in the surrounding area will come up with a wrong that needs righting.
When my players argue about what to do next in character while I leave the room, I know I'm doing my job as a GM in populating a world that my players care about enough to invest the time and effort to argue about the best course of action. My world has grown beyond the confines of my own mind and into the minds of my players, and that's a huge win. Nothing gives me more satisfaction as a GM.
So how do I give my PCs too much to do? Let them overhear rumors. Drop hints. Have them make enemies who want revenge. Offer paths. Hide hints and mysteries in a character's backstory. Give them an arc with several avenues to explore and questions to answer. Let them figure out that there's something making the barkeep edgy. Create another adventuring group in town and start a rivalry.
In short, offer your players a menu of adventure hooks and let them decide as a party what to focus on next. Make them feel that there's not enough time to do it all, then have the menu change whenever they take the time to tackle an adventure just to prove that their choices have consequences.
This sounds like a monumental task for any GM, but it's not all that bad. There are tricks to make it easier. Adventures can be retooled to fit circumstances so all that prep work won't go to waste. If they can reach a decision about what to do next at the end of a play session, you've got the time to flesh out the next adventure. Recurring villains tend to write themselves, especially if your players start giving you ideas in character followed by "That's what I'd do." Have a stable of side quests ready if the party needs a break from the main story arc.
Above all, don't worry that your players have destroyed your plans. Just because they're not following the script that you wrote for the adventure, that doesn't mean that all your preparation is worthless. The best plan never survives first contact with reality, never mind an enemy. Sometimes they capture the bad guy in the first act; just remind yourself that everything will be OK.
The "Overbusy PCs" approach requires plenty of prep-time work, but it needs to flexibly respond to the will of your players at run-time. For me, that's harmonious GMing, and it works for me. Roll with the punches and let your players write more of the story, because in the long run that's far more rewarding for everyone.
I'll be exploring some tips and tricks to GMing this way in future posts, so stay tuned.