Navigating an unknown area to find Something Important and make it back. Whether it’s the bark of the Singing Tree to make a talisman, or a lump of ancient ore, the effort of trekking through a new area, finding food and water, making shelter, and making it back home are all things that players could apply INT, WIS, DEX, and STR to over a session (or several).
Update: you have a lot of flexibility here to set the challenge rating without planning it all out. Instead, you adjust to the decisions of the players. If the players use some LOOT or ability to bypass some of the obstacle(s) and get the prize quick, they chose the EASY route. If they use some real creativity to do something unexpected, you might elect to grant them the HARD prize for their clever solution.
I’m reminded of the old Thundercats cartoon episode, The Trials of Lion-O. This is not an uncommon trope in storytelling, so there’s no shortage of examples you can pull from literature.
You could pit the players against one another in non-combat scenarios (first one to climb Crag Mountain Peak, first one to do all of Old Mara’s chores for her, whatever). You could pit the players against the old folks in town. Maybe they have to compete against last year’s winner(s).
You could implement individual challenges for the core abilities; or you could have an overall challenge that really needs a variety of skills to solve. The latter would help encourage the party to work together to use their individual skills for the betterment of the group – especially if there’s another team of coming-of-age youths against which they are pitted. First group to climb Crag Mountain Peak, harvest three pounds of Nettling Flowers (watch out for those sharp nettles!), and make it back home wins. Oh, sorry, did we forget to mention that the Nettling Flowers are the natural home to the Nettle Bees? etc etc.