Lessee, a few I've enjoyed:
The No Watering Can Run: pretty basic. (Optionally, you are allowed to take it out of storage for the volcano dungeon.)
The Decorating Muse: Start with a random appearance. By the end of spring, decorate your house to match. On the last day of spring, buy something from the traveling cart (preferably a furniture or decoration) and by the end of summer, upgrade your house and decorate the new room to match. Repeat for autumn and winter. During Winter, the bonus challenge is to buy items from the traveling cart at the night market all three days and use all three for a single shed's theme. Remember to check Pierre's and Robin's often for appropriate wallpaper and furniture accessories!
The Rip Van Winkle Run: Speedrun the trash panda. Named due to the fact that you sleep in for two years which is kind of fun in and of itself.
And you can get surprising mileage out of "try a farm type you've never done before, try a spouse you've never married before, try some skills you've never tried before" and really lean into it. Like if I were to do a challenge run for myself right this second? I'd go Trapper instead of fisher and see how "quickly" (in a strictly casual sense of the term) I can literally cover a Riverlands or Beach farm with crab pots.