Developer GrayStreet Partners has submitted plans to the city showing that the firm wants to construct a hotel on the site of the shuttered Pig Stand diner, a longtime Broadway corridor landmark. GrayStreet purchased the property at 1508 Broadway in February, around the time when the eatery’s owner, 76-year-old Mary Ann Hill, opted to close the restaurant so she could retire. The developer now wants to change the parcel’s zoning, according to the plan submitted on Oct. 3.