From the USGS Geographic Names Information System it looks like you've got a few choices for Blue Mountain:
Feature name Class County Lat. Long. State Elev(ft)
Blue Mountain Place Calhoun 334104N 0855034W AL 797
Blue Mountain Summit Calhoun 334052N 0854900W AL 1440
Blue Mountain Summit Cleburne 333019N 0854728W AL 1949
Blue Mountain Summit Monroe 352748N 0840605W TN 1709
Blue Mountain Summit Whitfield 344849N 0850205W GA 1316
Blue Mountain Summit Towns 344845N 0834518W GA 4009

Good Luck,
George