Rents are finally easing in parts of the South and Mountain West. Austin, Texas, saw the largest drop, with median rent down nearly 6 percent from a year ago. Rent prices in San Antonio, New Orleans, Denver, Phoenix, Tampa, and Salt Lake City also fell between 2 and 5 percent. Meanwhile, some cities are seeing the opposite: rents climbed 5 percent in Virginia Beach, Virginia and California’s Bay Area; 4 percent in Chicago; and 3 percent in St. Louis, where construction is constrained by space and zoning. Nationally, the median rent for new leases is down 1.5 percent from last year but still sits about 20 percent above pre-pandemic levels at $1,400 a month, according to Apartment List. A Harvard report shows a record…..