First, to clarify some points from above writeups:
No professional football team currently plays at Shea Stadium, but BOTH the New York Jets and New York Giants have played there in the past. The Jets had their home games at Shea from 1964-1983, before moving to the Meadowlands in New Jersey. The Giants played there for the 1975 season, the year before also moving to the Meadowlands.
The stadium is very close to LaGuardia Airport. While that might be charming to some (and I'll admit, I have sat in the top row of the stadium and looked at the planes land once or twice), it's generally annoying to fans and also to the players. Often, a pitcher will have to step off the mound, because of the distraction of a deafening airplane flying low overhead.
Strangely, no one has yet to mention where Shea Stadium is located. It's in the neighborhood of Flushing in northern Queens, New York. In addition to being near LaGuardia Airport, it's near the National Tennis Center (where the U.S. Open takes place annually) and Flushing Meadows-Corona Park (home of the 1939 and 1964-1965 World's Fairs).
The #7 subway line serves Shea Stadium, and was made famous by John Rocker's negative comments about its passengers in 1999.
Shea Stadium opened in April 1964. According to ballparks.com, Shea Stadium was:
Christened April 16, 1964, with Dodgers Holy Water from the Gowanus Canal in Brooklyn and Giants Holy Water from the Harlem River at the exact location where it passed the old Polo Grounds.
This goes along with the Mets' general scheme of mixing things from the Brooklyn Dodgers and New York Giants, who both departed for California in 1957 (the Mets' team colors are blue, for the Dodgers, and orange, for the Giants). As an aside, the water also is quite possibly the dirtiest "holy water" of which I've ever heard, but I digress...
After playing their first two seasons at the Polo Grounds in Manhattan, the Mets moved to Shea Stadium in 1964. In 2009, they moved to the new Citi Field, which is built adjacent to Shea.
Shea Stadium was demolished to provide parking lots for Citi Field.