Nationwide Network of Support for Veterans and Military Families Act of 2012 - Establishes the National Veterans Support Network to, among other things: (1) carry out national activities to raise awareness of the challenges facing military families and veterans, with related media campaigns; (2) provide support to communities that include veterans or members of the Armed Forces; and (3) encourage and promote participation by private organizations in activities that serve and support veterans. Requires the Network to establish a community support grant program to award grants to create or expand community-based veterans readjustment and support programs. Prohibits the Network from accepting any federal funds. Requires annual Network audits and reports to Congress.