Goitrogens are naturally-occurring substances that can interfere with function of the thyroid gland. Goitrogens get their name from the term "goiter," which means an enlargement of the thyroid gland. If the thyroid gland is having difficulty making thyroid hormone, it may enlarge as a way of trying to compensate for this inadequate hormone production. "Goitrogens," like circumstances that cause goiter, cause difficulty for the thyroid in making its hormone.
In people with normal thyroid function, goitrogens can induce hypothyroidism and goiter.  In those with hypothyroidism, goitrogens can further depress thyroid function and stimulate the growth of the thyroid (goiter).  In those with hyperthyroidism, goitrogens may suppress thyroid function. This may be a double edged sword if used as a treatment plan.  Goitrogens interfere with the uptake of Iodine by the thyroid. Limiting thyroid output by Iodine restriction can cause the thyroid to increase in size (goiter) in an effort to filter more blood to get more Iodine. Then the larger gland has the potential to produce more thyroid hormone when iodine is introduced back into the diet.
A better approach could be to increase copper metabolism by supplementation of copper and the assisting nutrients. Once copper is replenished and copper metabolism is working properly, the body will tolerate iodine without increasing thyroid hormone production. Copper is also closely connected to Iron and Vitamin C intake. A fine balance of all minerals, vitamins, and lipids is needed to ensure a completely healthy.

Many goitrogens are generally members of the brassica family. These include:
Broccoli               Cauliflower           Brussel  Sprouts              Cabbage
Mustard               Kale                     Turnips                            Rape seed (Canola Oil)
Other goitrogens include:
Soy                     Pine nuts                Millet                              Peanuts

Brassica family vegetables not only inhibit thyroid production, they also inhibit cancer growth. We know that sulfur, copper, and iron work closely together and that excessive sulfur can deplete copper and/or iron. Generally anemia is the result of low iron and/or copper. Also, foods and drugs that cause anemia also reduce cancer growth, indicating that the brassica vegetables might reduce cancer by inducing anemia.
The primary pre-condition for the production of thyroid disease is the onset of anemia. Brassica vegetables, with their high sulfur content, may be foods which induce anemia and consequently thyroid disease. 
 
Hyperthyroidism - Good and Bad

Food contains minerals which affect the thyroid.  As the hyperthyroidism is corrected, the foods on the avoid list will be tolerated better.
Also, a list of the foods that bother you can be a great help in determining what nutrient deficiencies you have and need to correct.

FOODS TO EAT
Beans                   Crab             Lobster             Nuts            Shrimp  

FOODS TO AVOID
Dairy - Excessive calcium to magnesium ratio increases rapid heart rate and tremors.
Garlic - Excessive zinc depletes copper.
Iodine containing foods -  Until copper is built up.
Licorice -  May be a toxic to the adrenals and thereby interfere with the sodium/potassium pump.  
Tinned foods, especially fish like tuna - bisphenol-A (an estrogen mimic) from varnish inside the can, increases heavy metal accumulation like mercury and cadmium which accumulate in fish and other sea foods.
Fruits, at least for a while - depletes copper
High carbohydrate diet- causes thyroid hormone increase to burn up excess calories.
Too many green leafy vegetables - high in cadmium
Rice - high in cadmium
Canola oil - interferes with normal thyroid functioning

SUPPLEMENTS TO AVOID

Zinc--depletes copper so you need to limit zinc until copper is   built up.
Iron--depletes copper so you need to limit it at the beginning, but it's essential for making hemoglobin so try to slowly introduce it after a few weeks of copper supplementation.
Manganese--Assists iron metabolism and a known copper antagonist. Introduce again if you go hypo.
DHEA
Pregnenelone
Grape seed extract
Proanthrocyanadins--from grape seed or pine bark.
Ephedra--found in weight loss and energy supplements.
Tyrosine--the amino acid that is the basis of thyroxine.
Arginine --stimulates growth hormone production which seems to stimulate thyroid hormone production.
Ornithine--same as Arginine
Licorice--depletes MAO which breaks down thyroid hormones after use.
Colostrum--seems to significantly increase hyper symptoms and may induce a thyroid storm.