Mesquite Town Square was the centre of Mesquite's beginings back in the 1900's with a handful of businesses, the first being the Interurban Depot in 1923. The stores originally faced the railroad tracks but as the town grew, they changed their openings to face the square. In all honesty, you could almost miss seeing the square its so small and insignificant looking.
There is a Texas site marker here which tells the story of Sam Bass (along with 4 others) who held up a Texas & Pacific train here in 1878. They took $152 but missed a hidden shipment of $30,000. In planning a bank robbery 3 months later, Bass was fatally shot by Rangers.