You'd think Baylor king Robert Griffin III would go wild after winning the Heisman Trophy this weekend in NYC -- but TMZ has learned, the star QB went straight to Ground Zero instead ... to pay his respects.

Griffin family sources tell TMZ, RG3 and several close family members made a beeline from the Best Buy Theater to the 9/11 memorial on Saturday. According to sources, the Griffins are a military family -- and Robert felt it was important to visit Ground Zero for some somber reflection.

We're told the Griffins spent a couple of hours at the memorial ... before heading downtown for a quick shopping excursion.

After the emotional tribute and the intimate family bonding time ... RG3 finally took off in his limo to party with fellow Heisman candidates Trent Richardson, Andrew Luck, Montee Ball, and Tyrann Mathieu.