What happened to Morgoth's original fortress after he was imprisoned? Was it completely demolished by the Valar? Did Morgoth just abandon it for Angband? What happened to it when Morgoth returned to Beleriand in the First Age?
It was destroyed
But not completely; the fortress itself was destroyed, so it was no longer a viable base of operations, but the tunnels and catacombs beneath were too extensive for the Valar to fully destroy or explore, and some of Melkor's minions hid there:
Long and grievous was the siege of Utumno, and many battles were fought before its gates of which naught but the rumour is known to the Elves. [...] The lands of the far north were all made desolate in those days; for there Utumno was delved exceeding deep, and its pits were filled with fires and with great hosts of the servants of Melkor.
But at the last the gates of Utumno were broken and the halls unroofed, and Melkor took refuge in the uttermost pit. Then Tulkas stood forth as champion of the Valar and wrestled with him, and cast him upon his face; and he was bound with the chain Angainor that Aulë had wrought, and led captive; and the world had peace for a long age.
Nonetheless the Valar did not discover all the mighty vaults and caverns hidden with deceit far under the fortresses of Angband and Utumno. Many evil things still lingered there, and others were dispersed and fled into the dark and roamed in the waste places of the world, awaiting a more evil hour; and Sauron they did not find.
The Silmarillion III Quenta Silmarillion Chapter 3: "Of the Coming of the Elves and the Captivity of Melkor"