Other animals are a good source!

Meat, eggs, and dairy all are good sources of iodine- and some organs especially liver. Apparently 1300 years ago someone in China had already figured out you could treat goiter by giving the patient ground up animal thyroid gland. Pretty cool.

https://en.wikipedia.org/wiki/Goitre#History

Also apparently in more iodine-rich soil, plants uptake enough to also be a good source, probably where the animals at lower trophic levels are getting it.