The mysterious site is the legendary energy and technology research facility, Project P.E.G.A.S.U.S. In the comics, P.E.G.A.S.U.S. stands for Potential Energy Group/Alternate Sources/United States. In the Avengers movies, no location is listed for the site.
Canon Marvel Universe Earth-616
Project Pegasus first appears in the Marvel Universe as a research site dedicated to discovering new energy sources and understanding alien technologies. The staff there were highly classified and possessed information regarding parallel and alternate realities. The site also functioned as a prison for supervillains with unusual powers. Several Marvel characters have served terms working security at the facility, including The Thing, Quasar (Wendell Vaughn) and most recently Darkhawk.
Created in Marvel Two-in-One #42 (August, 1978) by writer Ralph Macchio, Project: Pegasus was originally intended to research alternative (and unusual) forms of energy, but has also been used as a prison for super-powered individuals. The location of this facility is described as being in the Adirondack Mountains in New York State. -- Wikipedia -> Project Pegasus
Appearances in the Marvel Cinematic Universe
Staffed with scientists studying and creating energy technology and alien weaponry, Project P.E.G.A.S.U.S appears to be and underground S.H.I.E.L.D.'s research and development hub. Presumably there was more than one location of P.E.G.A.S.U.S after its destruction of a research center in Avengers.
Project Pegasus is alluded to in Iron Man 2. Tony Stark is shown opening a wooden crate (1:24:04) marked "Project Pegasus" in preparation to synthesize a new element.
Additionally, in the tie-in prelude comic to the Avengers, the World Security Council mentions that funding is being redirected from S.H.I.E.L.D (with help from NASA) to a new operation, codenamed Project P.E.G.A.S.U.S, in the aims of analyzing the Tesseract.
Marvel has decided to release more information on Project P.E.G.A.S.U.S. in their new digital comic release Fury's Big Week, a prelude to the incidents in the Avengers movie.
On Sunday, Marvel are launching a new digital comic book that works as a prelude to the upcoming Avengers movie, Marvel’s The Avengers Prelude: Fury’s Big Week and will sit along the other Marvel’s The Avengers Prelude comics.
Set in Marvel Studios movie continuity, it’s the first of 8 issues, subsequent issues will run on Tuesdays for 99 cents an issue. It has been written by Chris Yost and Eric Pearson and drawn by Luke Ross. And it mentions a certain Project P.E.G.A.S.U.S. and it’s relation to the cosmic cube from Thor.