4001 N. 23rd St, McAllen. McAllen Public Library. (956) 255-0190. The McAllen Farmers Market provides access to locally grown vegetables and value-added products. Open Saturday 10:00 to 1:00 pm. The McAllen Farmers market is a non-profit 501(c)(3) has been providing shoppers access to locally grown and produced foods since 2007.