Dissolve sugar in warm water. Sprinkle yeast on top of the sugar water mixture and let it sit for 10 minutes to proof. Meanwhile, combine whole wheat flour, all purpose flour and salt in the bowl of a stand mixer fitted with a dough hook.
Stir yeast into water and add vegetable oil. Turn mixer on to low speed and slowly pour in water/yeast mixer. Increase speed to medium low and knead dough until smooth. Form dough into a ball and place into an oiled bowl. Cover with plastic and let rise for about 2 hours.
Punch dough down and form into a rope. Cut rope into 8 equal pieces (see note). Roll each piece into a circle that is approximately 1/4" thick. Cover with a clean dish towel and let rise for 30 minutes.
Heat oven to 500°F. Place 2-3 pitas on a wire cooling rack, and place rack directly into oven. Bake for about 5 minutes until pitas become very puffy and just begin to brown on the top. Remove from oven and cover with a clean, damp dish towel until soft. Repeat with remaining pitas.
To serve, cut a slit into an edge with a sharp knife or cut in half to make a sandwich. Can also be cut into wedges to serve with dip. Store in a sealed bag at room temperature for 1-2 days or in the freezer for around a month.
Notes
If you want smaller pitas, cut into 10-12 pieces. If you want larger pitas, cut into 4-6 pieces.