Where is Graviton Core Delta?

Academia -400 AF-, while complex, is fairly linear. When you arrive, the only direction you can go in is towards the northwest into the Alley. Past the Alley, you'll go to the Grand Avenue, which wraps around to the east and north.

In the far west of the Grand Avenue, there's a fairly long, linear path that takes you to the western side of Academia, where New Town is.

New Town is a bit of a circle (Chocolina is marked by the o):

+---------  +
| To gate   |
| +-------+ |
| | +-+---+ +-----+
| | |x|   |      =| <-- blocked for now
| | | | +-+-----+ +---------------------
| | | | |       | From the Grand Avenue
| | | | |       | +---------------------
| | |o| |       | |
| +-+ + |       | |
|     | |       | |
|     | +-------+ |
|     |           |
|     +---------+ |
|                 |
+-----------------+

The Graviton Core Delta is phased out the northwest area (marked by the x): make your way to Chocolina, move north along the ramp, and pop Mog's Moogle Hunt ability until you get it.

Note the Graviton Core Delta is not accessible until:

You defeat Zenobia.