Unless you are very aware of the source of the iodine rich foods you are considering we advise using a supplement. Though whole foods are always better for us, the problems in Japan and Asia make our sources of such things as seaweeds etc. very tenuous right now due to the radiation there.
Dr. Sircus recommends using either nascent iodine or Lugol's iodine... the tablet form of Lugol's is called Iodoral and comes in a high dose of iodine.
You will need to read Dr. Sircus' book on Iodine available here:
which gives full explanations of both types of iodine so you can better decide which is right for you.
In addition, you can obtain a personal consultation with Dr. Sircus if you feel you need more guidance.
People with hypothyroidism can improve greatly with additional iodine supplementation and supporting supplements and often find they can decrease the amount of pharmaceutical medicine they are taking or even no longer require it.