Indianapolis City Market 222 E Market St, +1 317 634-9266. [203] Indy's favorite historical landmark to dine! Open only for breakfast and lunch stop by here for a great cheap meal. From Cajun to Greek, gourmet potatoes and roast beef sandwiches. Tons of restaurants and merchants make this a multi-level historical edible experience. Dine outside to enjoy the historical area and watch the locals buzz around on their lunch breaks.