What should I do with nuggets?

I visited the quarry and acquired some silver & gold nuggets. I'd like to sell them, but only if there's nothing more useful I can do with them. I also am not sure where to sell them since the Nooklings won't take them.

What should I do with my nuggets?

The five items you break out of rocks at the quarry (or 'minerals', as the game calls them) are not added to your inventory; they are simply a measure of the relative success of your quarry visit, and the resulting payout.

The minerals you can find in rocks are as follows:

• Various gemstones: Good
• Silver nuggets: Better
• Gold nuggets: Best

How well you did determines how much of the featured item you collect after your visit, whether that's themed essence (like Cool, Cute, Modern, Harmonious, etc.), a custom crafting material (such as the Mario event mushrooms, the holiday candy canes, the various gyroidites, etc.), or bells. Note that you will also get bells even if bells were not the featured item at the quarry during that period; for that matter, you will generally get more bells for doing worse. This appears to be a sort of protection against bad luck so that the value of quarry visits remains relatively stable. Because of this, I try to avoid going to the quarry when the featured items are bells, since bad luck on a bells-only visit awards nothing extra.