"My wife loves precious metals."
Translation:Má žena miluje drahé kovy.
"Vzácný" is more akin to "rare" and is less common in this context. Drahé kovy is a technical or scientific term.
But the corpus shows that vzácné kovy is used as well but be aware it can well mean different elements like cobalt or lithium. I will add it for this reason. NOT because precious means vzácný, but because one can find enough occurrences of "vzácné kovy" with the meaning of gold, silver, platinum...