One thing I always try to find whenever I visit a ballpark is the park's dedication plaque. Most ballparks have them, but they're sometimes difficult to find.
Shea Stadium's plaque was located near the Gate E ticket window. Like all dedication plaques, Shea's shows its full proper name (William A. Shea Municipal Stadium). In addition, the plaque highlights the civic leaders of the time starting with the NYC mayor, comptroller, etc. Also listed was Robert Moses. While he played a large role in the Dodgers and Giants leaving New York in 1957, he was also the main proponent of the placement a ballpark in Queens. The site was actually offered to the Dodgers, but they declined and moved to Los Angeles.
Also listed on the plaque is Shea Stadium's Engineer/Architect Praeger-Kavanagh-Waterbury. PKG was involved in the design of other ballparks such as Dodger Stadium and the 1970's renovation of Yankee Stadium.
Finally, the most important item listed on the plaque is the year of dedication, 1964. These plaques are often overlooked, but they're something I always look for when visiting a park for the first time.