Rice is a grain, correct, although you have to use what right for you, what is my poison might be just fine for you, so try out some rice (i might recommend brown over white, depending on your body comp and goals).
I also use potatoes as carbs sources (mostly sweet potatoes, but sometimes red ones)
Ezekiel bread is a grain, but its different from most breads in that it is low glycemic (36 on the glycemic scale). I go back and forth with eating ezekiel, but ive just had a hankering for it lately, so its up to you.
ill also note I base alot of my diet off glycemic index and load, and how foods are effecting my blood sugar. Again, based on you and your goals this may, or may not apply to you.