I like that you said "limit" and not "cut out completely". I'm doing the same...limiting. I replaced the white bread at home with whole wheat (we'll see how the kids take to that) but when we eat at Subway, they use refined breads and I think they're still a healthy choice.
I can skip bread altogether pretty easily, but I like potatoes. I'm buying more sweet potatoes and fewer white potatoes for the same reason that I'm switching breads. I'm also trimming the toppings on all veggies and have discovered recently that veggies are tasting more flavorful than they used to. I'm sure it's because my tastes are changing as a result of my choices.
I hope you find "healthy" foods to be more flavorful as well as you make the switch.