Goldfinches feed primarily on weed seeds, and sometimes insects when they are available. For this reason, goldfinches love weedy fields, orchards, open woodlands, thickets and roadsides, especially if they contain patches of thistle and sunflowers. In other words, they may prefer eating these seeds right off the plant, instead of in a feeder, so you could plant some of these plants near the bird feeder.

Here’s a map of the presence of the American Goldfinch:
Yellow = Summer only
Blue = Winter only
Green = Year round

So, it really depends on where you live and what time of the year it is. Hope this helps.