Soy can be things like tofu, soy milk, edamame, and soy burgers but a lot of products may contain soy so you have to check labels to see.
There are certain foods that if you are very *brittle* on your meds - as in you are going up and down and all over, perhaps you should avoid soy and goitrogenic foods such as uncooked cabbage, broccoli.
http://www.ehow.com/how_2319202_that-may-hurt-thyroid-gland.html
Now, foods high in iodine
http://www.weightlossforall.com/foods-rich-iodine.htm
I was told to avoid them (like shrimp) but some are told to have more of them - so you need to ask your doctor for your case.
Make sure you are taking your medication consistently as that helps.
I have hashimotos diesease. I finally lost my hypothyroid weight after several years initially using the South Beach diet. It took me about 4-5 months before I realized the results and assured they were profound.
I second the comment regarding taking your meds at a consistent time. This allows your body to maintain equilibrium and perform internal processes more efficiently, thus giving you more energy to burn calories and feel better as a whole.
I, too, have Hashimoto's and have been struggling with my weight. I have a double whammy in that I have also had a complete hysterectomy (9 years ago) and take Estradiol.
My doctor hasn't said too much to me about avoiding certain foods, but did not like the supplements I was taking that contained kelp and algae. So, have changed my supplements to products from Thyrolife. An endocrinologist here in Houston sells the brand.
Also, the doctor asked me what kind of water I take my with my Synthroid. He asked me if I am drinking water with minerals. I have tried to drink the distilled, but cannot, upsets my stomach.
This is all so much fun.........