Kelp

Yogurt

Milk

Eggs 

Strawberries 

Mozarella cheese

Carrots 

spinach

apricots

asparagus

olive oil

avocado

sunflower seeds

whole grain cereals

bananas

oily fish

Selenium

It is also believed to help if you increase your selenium intake. This can be done by eating foods such as whole wheat bread, bran, Brazil nuts, tuna, onions, tomatoes and broccoli. Include some of these foods on a regular basis.

Iodine With Vitamin E

When people with underactive thyroid glands take 4mg of iodine and 600 units of vitamin E, it has been found that the amount of iodine taken up by the gland increases and the quantity of thyroid hormones in the blood also increase "almost immediately and markedly".

Zinc

An Italian study shows that supplementing the diet with zinc improves thyroid function. Many patients with hypothyroidism have low levels of zinc, and the study demonstrated that over 50 percent of patients given zinc supplementation experienced improved thyroid function which reduced the incidence of clinical hypothyroidism.

Restore Thyroid hormone production naturally with the guaranteed Thyromine Thyroid Formula.

Generally:

Follow a diet with at least 50 % of the foods being fresh, and organically grown to rebalance and establish a better metabolism. The enzymes from live foods help the body to maintain proper metabolism. Foods that heal include sprouts, salads, raw vegetables, and thermos cooked grains to retain enzymes which heal and feed the glands.

Eat foods rich in vitamin A, such as yellow vegetables, eggs, carrots, and dark green vegetables. M.U. Tene is concentrated Beta-Carotene, the precursor to Vitamin A and one of nature's most powerful antioxidants.

Iodine rich foods that nourish the thyroid are: fish and sea vegetables such as: arame, kelp, dulse, hijike, nori, wakame, and kombu. Seaweeds are very nourishing to the glands.

Zinc and copper are important in helping the body make thyroid hormone. Foods rich in zinc include: beef (range free), oatmeal, chicken (range free), seafood, dried beans, bran, tuna, spinach, seeds, and nuts. Foods rich in copper include: organ meats (range free), eggs, yeast, legumes, nuts, and raisins.

The amino acid tyrosine is helpful. Tyrosine is found in soy products, beef, chicken, and fish.

Black and red radishes have been used by some doctors in the old Soviet Union as accepted medical treatment for hypothyroidism. Raphanin, the main sulphur component in radishes, is chiefly responsible for keeping the production of thyroxine and calcitonin (a peptide hormone) in normal balance. Seeds and nuts, seed and nut milks, vegetable juices (celery, parsley, small amount of carrot, Swiss chard, wheat grass) and plenty of green drinks containing chlorophyll for healthy blood are helpful. Earth's Harvest is a blend of three micro-algaes that are a rich whole food source of chlorophyll. Having a mixed vegetable juice that includes the juice of a few radishes, carrot, tomato, celery or zucchini, with a pinch of kelp may benefit the thyroid gland greatly. This juice can be blended in a blender for those who do not have a juicer.

Black walnut has a high content of iodine and is a thyroid stimulant.

Other beneficial ingredients for vegetable juice combinations include: alfalfa, all leafy greens, beet tops, carrots, celery, green peppers, parsley, seaweeds, sprouts, and watercress.

 Restore Thyroid hormone production naturally with the guaranteed Thyromine Thyroid Formula.

Also, for the Mayo Clinic:

Goitrogens and  foods are they found

- soybean-related foods and

- cruciferous vegetables.

- peaches, strawberries and millet -

cabbage, kale, broccoli, kohirabi, mustard, lima beans, linseed, sweet potato, peanuts, soy products

- Broccoli (uncooked, Brussel sprouts, Cauliflower, Mustard, Rutabaga, Turnips, Millet, Peaches, Radishes, Soybean and soy products, including tofu Spinach Strawberries

Avoid caffeine drinks like coffee, cola; avoid stimulants like smoking and alcohol as these all effect the thyroid function.

From another source:

Here are the top 10 foods you should avoid if you suffer from an underactive thyroid symptom. While this list is not all-inclusive, it gives some basic guidelines to follow. Here are some helpful suggestions on what not to eat:

1. White breads - White bread does not contain significant nutritional value and for some people can contribute to difficulties with insulin resistance and hormonal problems.

2. Caffeine - examples include, but are not limited to, coffee, soft drinks, hot cocoa, chocolate and some herbal teas. All of these delicious comfort foods or drinks will depress proper thyroid function and can make your underactive thyroid symptom worse.

3. Broccoli - don't eat this raw or cooked. Broccoli is considered a goitrogenic food which means that consuming broccoli can increase the likelihood that you'll develop a goiter somewhere on your body. This would be due to decreased thyroid hormone production.

4. Peaches - also considered a goitrogenic food, be sure to add this food to the list of ones that can possibly cause a goiter to form due to your thyroid's hormone production being decreased.

5. Peanuts - yes, they are salty, crunchy and delicious, but they aren't the best snack choice for someone with an underactive thyroid symptom, as they interfere with the production of thyroid hormones.

6. Fluoride - this is found in toothpaste and drinking water that comes from the tap. Fluoride essentially blocks iodine receptors in the thyroid gland which causes reduced iodine-containing hormone production.

7. Chlorine - not only for pools, it is found in pretty much everyone's drinking water that comes directly from the tap. Like fluoride, chlorine also blocks iodine receptors in the thyroid gland, causing reduced iodine-containing hormone production. So, drink plenty of distilled or purified water.

8. Soy - soybeans are off limits, as they have an anti-nutrient that contains a chemical which reacts with iodine. Since iodine is critical to make the thyroid hormone, this food should be avoided if you have an underactive thyroid symptom. Soy milk, soy flour, and tofu are also foods to add to the do not eat list.

9. Garlic - it may keep people away and it's great in spaghetti sauce. However, garlic also reduces iodine uptake in the body.

10. White flour - in the same family as white breads, this is a food that can, for some people, contribute to difficulties with insulin resistance and hormonal problems. White flour is a refined and over-processed food and has very little, if any, nutritional value at all.

Generally, avoid refined foods, saturated fats, sugars, and white flour products. If the thyroid problem is severe it is then good to avoid brussels sprouts, cabbage, broccoli, kale, mustard greens, peaches and pears as they have anti-thyroid substances and may suppress the thyroid function.

From the Mayo Clinic:

You don't need to follow a special diet if you have hypothyroidism as long as you take thyroid hormone replacement as directed by your doctor. Many Web sites promote hypothyroidism diets that supposedly increase thyroid function by adding or eliminating certain foods. But there is no evidence that these hypothyroidism diets work.

The important thing to remember about hypothyroidism and diet is that certain foods, supplements and medications can impair absorption of synthetic thyroid hormone. These include:

• Iron supplements or vitamin supplements containing iron
• Calcium supplements
• Soybean flour
• Aluminum hydroxide, a popular antacid
• Sucralfate, an ulcer medication
• Some cholesterol-lowering drugs, such as cholestyramine and colestipol

- naturally-occurring substances that can interfere with function of the thyroid gland. - soy extracts, and foods made from soy, including tofu and tempeh. Isoflavones in soy are associated with decreased thyroid hormone output. Isoflavones are naturally-occurring substances that belong to the flavonoid family of nutrients. Flavonoids, found in virtually all plants, are pigments that give plants their amazing array of colors. Most research studies in the health sciences have focused on the beneficial properties of flavonoids, and these naturally-occurring phytonutrients have repeatedly been shown to be highly health-supportive. Reduce thyroid hormone output by blocking activity of an enzyme called thyroid peroxidase. This enzyme is responsible for adding iodine onto the thyroid hormones.

- cruciferous food family.  broccoli, cauliflower, Brussels sprouts, cabbage, mustard, rutabagas, kohlrabi, and turnips. Reduce thyroid function by blocking thyroid peroxidase

The best advice is to take synthetic thyroid hormone on an empty stomach and several hours before or after these particular foods, supplements and medications to avoid potential interactions.