Yes, it is a good idea to patronize the small restaurants on the outskirts of the hutong, but here is another tip. Go to the very fanciest restaurant possible, in a fancy five-star hotel. Then order the cheapest items on the menu. That likely will involve some vegetables (pumpkin in egg, anyone?), tofu, and fried rice. It will be an amazing meal, quite possibly better, at least to a Western palate, than if you had ordered the most expensive delicacies of that restaurant. Many of these courses will not exceed $10 per shot, which is still about at American prices or even slightly below, and that’s not adjusting for massive differences in quality. If you feel you can afford more than that, fine, but the low budget constraint actually directs your attention to some pretty fine items, and to items which are never truly good in American Chinese restaurants.
I’ve had good street food in Beijing, but in my view it is neither your first nor even your second preferred option.