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Location: Royal Palace Throne Room, Tienius Delitian, or Temple Reception Area, Fedris Hler
After the attack, depending on who you report to, Tienius Delitian or Fedris Hler, they'll send you to investigate the uncovered dwemer ruins of Bamz-Amschend and report back to them what you find.
If you go back to Plaza Brindisi Dorom to the rubble at the top of the fountain, you'll find a ladder leading down. This is the entrance. Once inside, walk through the cave-like corridor to the edge, and down below you'll witness Dwemer constructions fighting the same weird mechanized creatures you recently fought on the surface, and your journal will update. There's no sense in going down yet, but you can if you want to. Beware of the Centurion Archers, as they pack quite a punch with their Dart. Tips in the "A Show of Power section".
Report to either Tienius or Fedris, depending on the path you chose. Tienius will ask you to speak to the King Helseth himself, who has appeared for the first time in the Throne Room. Fedris will ask you to speak with Almalexia.
They both will give you another quest, but I'll outline paranoid King Helseth's quest first, "An Assassination Attempt", and then at any time, you can speak with Almalexia for her next quest, "A Show of Power", which you'll find in the walkthrough a few steps below this one.