"My son eats anywhere."
Translation:Mijn zoon eet overal.
A better translation of ergens is somewhere (that's why it doesn't work). Right now I cant think of any context where anywhere is a translation of ergens, so better forget about it. It's better to see words in their context, than finding all possible translations in a dictionary.
I'm not sure if this is correct, but in the "Zien jullie mijn bril ergens," Ergens, referring to somewhere/anywhere, is in the case where the glasses are in only one place, somewhere. But in "Mijn zoon eet overal," Overal, referring to anywhere, is the case where anywhere is all/many places. That's how I see the contexts being different.