Randall's Island Municipal Stadium, built by the WPA[1,4,6], scene of final 1936 men's Olympic trials, where Jesse Owens qualified to go to the Berlin Olympics. The 1936 Olympic swimming trials were held at another WPA-built site, Astoria pool in Queens.

See Wikipedia for a brief history of the stadium and its many name changes. It was torn down in 2002 and replaced by the much smaller Icahn Stadium, named after the billionaire who paid for it.

On June 19, 1936, the Parks Department announced the opening of the Randall's Island stadium, with tickets available for the final American Olympic men's track and field tryouts on July 11 and 12, reserved seats costing 75 cents, $1.00, and $2.00 (see press release); 15,000 tickets were sold. The first day of the Olympics tryouts was preceded by an opening ceremony presided over by Robert Moses and featuring Harry Hopkins, FDR's federal relief administrator, and Mayor La Guardia.

Lest there be any doubt as to the stadium's WPA pedigree, Robert Moses states (in response to a reference to its "shoddy construction" in the NY Sun), "The statement that it was a poor piece of construction work is ... false, as is the statement that it would not have been accepted by the city if it had been done by contract. As a matter of fact, exactly the same standards are applied to acceptance of WPA work as for acceptance of any other work for which I am responsible" (see the Parks Department press release for this and a great deal more commentary on the matter).

In its first year of operation, the stadium hosted not only the Olympics trials, but also local track and field meets, folk dancing exhibitions, Irish hurling games, amateur baseball games (schools, corporate leagues, etc), a junior Olympic carnival, the anti-fascist World Labor Athletic Carnival ("Counter-Olympics"), soccer matches, college football games, professional football games, major and minor league baseball games, Negro league baseball games, rugby games, barbershop quartet competitions, and who knows what else (this list was culled mainly from the 1936 Parks Department press release archive). In 1938 it hosted the Carnival of Swing[2,3], a memorial concert for George Gershwin, featuring the big bands of Duke Ellington, Benny Goodman, and Count Basie, among others, considered to be the world's first outdoor jazz festival.

1. Moses Gets Funds for City Stadium, New York Times, Thursday, September 12, 1935, p.27. “Park Commissioner Robert Moses disclosed yesterday that he had obtained funds for the construction of the proposed $1,000,000 stadium on Randalls Island despit the refusal of Public Works Administrator Harold Ickes to permit the use of Triborough Bridge funds for the project. The money for the stadium, which will have permanent seats for 40,000 spectators and is to be opened in July of next year for the Olympic track and field tryouts, will be obtained in part from city relief funds and in part from the Works Progress Administration. The cost of the structure includes $500,000 for materials and equipment. Mayor La Guardia, who favors the plan for a municipal arena, has agreed to let the Park Department use $250,000 of non-reimbursable relief moneys, that is, moneys furnished wholly by the city. The WPA has allotted a similar amount for the project for materials and equipment and will expend $500,000 for labor.”
2. Carnival of Swing, Wikipedia, accessed 14 September 2017.
3. Carnival of Swing, video, Youtube, accessed 14 September 2017.
4. Opening of New Municipal Stadium, NYC Parks Department Press Release, July 1, 1936, notes the presence of Harry Hopkins (WPA Administrator) as a speaker.
5. $1,000,000 Randalls Island Sports Project Impresses Olympic Officials, New York Times, May 8, 1936, p.28. “Two thousand men work on the project in three shifts, with the working time twenty-four hours a day, seven days a week.”
6. Hopkins Talk Here July 11, New York Times, Sunday, July 5, 1936, p.67. “The program for the opening of the new municipal stadium on Randall's Island on July 11 at 2 P.M. has been announced by the Parks Department. Harry L Hopkins, Federal Works Progress Administrator, will be the principal speaker at the dedicatory exercises, at the close of which at 2:20 o'clock the Olympic trials will get under way ... The Randall's Island stadium was built with WPA labor, the city furnishing some of the funds for materials.”