There is no train to Badaling in fact. If you are afraid of the transit from one bus to another, you can just rent a car. it is sunny these days in Beijing, and the temperature is 4-13C. Local delicacies in Beijing are numerous like Mungbean Milk, Fried Bread Circle, Rolling Donkey and Sticky Rice with Sweet Stuffing.
For dinning in Beijing, you can knwo more from https://www.travelchinaguide.com/cityguides/beijing/dining.htm