I don't go out of my way to avoid any particular food because I don't feel that I consume enough of the goitrogenic foods on a daily basis to impact my thyroid. Most of us eat things in moderation, but if there's something on the list that you heavily consume you might consider decreasing some. Things like Brussels sprouts, rutabaga, turnips, kohlrabi, radishes, cauliflower, African cassava, millet, babassu (a palm-tree coconut fruit popular in Brazil and Africa) cabbage, and kale are all considered goitrogenic. Cooking breaks down the foods some, and they are much less goitrogenic when cooked. The foods that I eat a lot of like broccoli are usually cooked, so I don't stress too much about it.
Here's an article about soy. I think the jury is still out on it, but I think that the concern is more for things with highly concentrated soy (like infant formula and supplements) affecting the thyroid than moderate consumption of soy foods:http://thyroid.about.com/cs/soyinfo/a/soy.htm
Foods with selenium promote a healthy thyroid. Good sources of selenium in your diet include: wheat germ, seafood and shellfish, beef liver and kidney, eggs, sunflower and sesame seeds, brazil nuts, mushrooms, garlic, onions, and kelp.
I don't necessarily go out of my way to add these to my diet, either, but if my thyroid levels were constantly going up and down I would look closer at my diet. The most important thing is to take the medication on an empty stomach to maximize absorption. This is one of the most comprehensive articles I've read about when to take the meds:
There was one time my labs showed that my TSH was elevated more than normal. My endocrinologist suggested some changes to how I was taking it prior to upping my dose. I made the changes (take it on an empty stomach, about same time each day and without any vitamins that contain iron) and at my next visit the labs were better and my medication didn't need adjusting at that time.