You just have to wait for DIY recipes that use them! In particular the recipes that you get from Celste seem to use them. Don't worry though, the recipes that do use them are pretty cool so I would not sell them!
So far, I've managed to get recipes for the golden slingshot and the golden watering can, and I don't think the golden slingshot is worth the cost of using up a gold nugget. I was dismayed to find out first-hand that golden slingshots do break. My golden watering can hasn't been broken yet, but it takes me a long time to break a watering can. My wife has built a golden wand that is so far unbroken. Neither my wife nor I have broke a wand of any type yet, so a golden wand might be a good way to show off your bling.
My opinion is that it's best to save the gold nuggets for the furniture, walls, and flooring recipes that need them.
For the golden series, all of the Zodiac set, the Robot Hero, and Golden tools (I recommend just making them once for the miles cause it's costly and they're not really worth making more than one)
It took 18 gold nuggets to make the giant robot (8 for the gold armor you need to craft it & 10 to craft the actual robot). I used 4 to make a gold lucky cat & quite a few to craft gold tools, but I only have the gold shovel, slingshot & watering can so far.
Don’t sell them! In addition to gold tools, you’ll get lots of DIY recipes that require gold nuggets.