If you have some gold to sell, you can usually take it to a coin shop. Pawn or jewellery shops too, but they usually won’t pay as well. If you come across a large nugget, weighing several pounds so that it’s worth tens or hundreds of thousands of dollars, it’s probably be best to take it to the mint, since a coin shop won’t have that kind of money on hand.
What do you do for platinum? You find a large nugget of native platinum, where can you take it to sell?
When I salvaged some bits of platinum/iridium wire that I collected for several years from some electrodes used in medicine, I was offered spot gold prices, which at the time was less than platinum. But it amounted to less than an ounce, so that probably figured into it. I bet for larger amounts you could get closer to spot platinum, which is currently less than gold. The place I took it was a local metals dealer, but coin dealers often deal in various forms of precious metals.