The Arch-Mage is up there because of a dragon attack. How do I get up there? I am in the first quest, Under Saarthal. I am playing on the Xbox 360.
If you're in the part of the Under Saarthal quest where you are asked to meet with the Arch-Mage, Savos Aren, then just go to the Arch-Mage's Quarters (first door to the left upon entering the Hall of the Elements [the training chamber]), which should now be unlocked.
If for some weird reason, Savos Aren is not there, like due to the dragon attack you mentioned, then kill the dragon who is attacking, which should make Savos Aren return to his original routine. Then use the wait function and check if Savos Aren walks back to the Arch-Mage's Quarters.