Post-9/11 Veterans Educational Assistance Improvement Act of 2010 - Revises provisions concerning the Department of Veterans Affairs (VA) post-9/11 veterans' educational assistance program to, among other things: (1) revise definitions concerning eligibility, and include certain National Guard service as service qualifying for such assistance; (2) revise assistance amounts (including monthly stipends), and types of approved programs of education; (3) allow the pursuit of educational programs at institutions other than institutions of higher learning, including on-job training and apprenticeships, flight training, and correspondence courses; (4) provide an assistance amount for programs of education pursued while on active duty; (5) provide an annual effective date for stipend rates; (6) repeal the limit on the use of such assistance for the payment of only one licensing or certification test; (7) allow the use of educational assistance for the payment of national admission tests and tests for determining course credit; (8) bar the duplication of benefits under certain VA educational assistance programs; (9) bar the concurrent receipt of educational assistance benefits transferred to children; (10) allow the Secretary of Veterans Affairs to make certain subsistence allowance payments to enrolled veterans when an institution is temporarily closed; (11) increase the amount of the reporting fee paid by the Secretary to an institution for providing information concerning an individual's enrollment in a program of education; (12) limit assistance benefits to individuals who enlisted or reenlisted before October 1, 2012; and (13) revise cost-of-living adjustments under the Montgomery GI Bill educational assistance program.