I just played the Strange City stage for the first time, and completed the task. Who do I talk to now? It seems as though I have tried everyone. It's near the beginning of chapter 4.
Try going to the bar and asking for some quests there. OR going down stairs where the bar is to the infirmary. I think you have to talk to that chick once at one point.
Speaking of Phantom Dust, did you have real problems with the 2nd last mission of chapter 3, "Edgar's Memory"? It was a 2v2 fight with Alpha and Chunky trying to find find a memory box. And for some reason Chunky was BEYOND useless in this mission. He hardly fought at all, and he would never help me. Many times he would run right past one of the enemies! Meanwhile I was getting CONSTANTLY double-teamed by both of the bad guys. It took me more than 20 tries to finally finish that mission. I didn't have any problem with the other ones before it. But that one... one guy would paralyze me, and the other would bomb the crap out of me, almost every time. Of course it didn't help that my best spells were arcs (Psycho Spear) and crawl (Root)... and both the enemies were rollers.
God damn Chunky. I wish I could have dropped him off that cliff and left him for dead. If I never do another mission with Chunky as my partner, it will be too soon.