Jambonz Grill & Bar in Sturgis has excellent food. it is just up the street form the south exit into Sturgis. They have both inside and outside seating. The burgers are really good.
Go north out of Sturgis on 79 past the new Broken Spoke and look for a sign that says Vale and turn right follow it down to an old school on the left and they have great food [ plate lunches ] and beer for a decent price.
I second the idea of the old fashioned diner in Hill City. It has great food and not the expensive. You'll see it on main street towards the south end of town.