I would caution these women against looking to sea vegetables or fish as a dietary source, as they can be highly contaminated by heavy metals and radioactive contamination - even today the Fukishima disaster remains unresolved, the contamination continues. I'm not necessarily suggesting that these women cut all sea vegetables and fish out of their diet, but rather that they exercise prudence in their choice of products and moderate consumption.

Recommendations would include:
Moderate amounts of organic cranberries or juice. Excessive cranberry consumption can lead to the formation of kidney stones.

Cage-free eggs.

Organic skin on potatoes. Conventionally grown root vegetables 'sponge' up all those excessive pesticides that have saturated the earth they are grown in.

Organic yogurt.

I'm sure there are others. Dried prunes aren't terribly high in iodine but are a decent source, and are also a good source of boron and vitamin k; they could also be good to have on-hand post labor for other reasons :) Our boron deficient soil and that mineral's important role in the proper mobilization of calcium and magnesium is a post for another day though.

I would recommend that the above foods be added to the diet in a complimentary role, but not be viewed as adequate replacement of a standard prenatal vitamin that also contains iodine, selenium, and either a natural form of folate or folinic acid instead of folic acid. Cheers.