Old chinatown was near midtown, there are remnants of it left, but the newer, bigger chinatown is up and down bellaire near the beltway.
Asian cultures don't really eat American "breakfast foods" for breakfast, so the breakfast places that would be around there would just be the usual american chains like IHOP, etc.
Some people like to eat dim sum (dumplings) for breakfast or brunch, and Dim Sum King (9160 Bellaire - just inside the beltway) is pretty good and reasonably priced.