Japan is so full of restaurants that you can hardly walk a block without running into a noodle shop.
My advice is just to walk around, looking at the window or outdoor menu displays, and pick something that looks intriguing.
I don't know what you mean by an American-style breakfast. Here are some of the options:
1. McDonald's, with the options as back home and picture menus you can point to
2. A bakery that serves rolls and coffee or a Mr. Donut
3. A "Jonathan's" family restaurant (with picture menu to help the kanji-illiterate foreigner)
On the other hand, your hotel may offer a multinational breakfast buffet.
If you're afraid of getting rice and miso soup for breakfast, that's actually not easy to find unless you're staying in traditional accommodations such as a ryokan or minshuku. It may be an option on your hotel's breakfast buffet, but of course, you can always ignore it.