Tony remembers (just about) that his dad, Howard Stark, told him that he worked there with Hank Pym in this period.
(As As Tony says in Civil War, his dad mentioned knowing Captain America a lot; and as we see a bit in Iron Man 2, he probably tried to tell Tony a lot of useful stuff about his work that Tony largely ignored but sometimes vaguely remembered. AndFinally, as Nathan K. points out, the date they go back to is shortly before Tony's own birth, so it's not surprising Tony has a good idea of when his dad and Pym were there together.)
This meansAs Pym is present, they can get both the Tesseract, and the extra Pym Particles they need to get the Tesseract back to the present (as originally they only had enough for one round trip each).
The base is actually Camp Lehigh, the army base where Steve Rogers trained before becoming Captain America, so it’s kind of special for him. (A sign is visible outside the base declaring it the birthplace of Captain America.) The SHIELD facility within is the same bunker that Cap visited in The Winter Soldier, which thenat that time housed the digitised Arnim Zola.
But only Tony was aware of the likelihood that both the Tesseract and Pym particles were there at that time.