After completing the Innocence Lost quest, I came by Riften's Honorhall Orphanage to adopt a child.
After entering the orphanage, I noticed that there wasn't Constance Michel – the new keeper of the orphanage.
I looked all around the Honorhall Orphanage but still not luck. Does she go to her home or something in the lines of that?
Best Answer
After killing Grelod, Constance Michel enters a state of panic (although will not attack the Dragonborn), or will walk out of the orphanage and insist that the Dragonborn leave (even if spoken to outside). Although, after the Dragonborn speaks to Aventus Aretino to officially complete the quest, Constance should calm down and remain in the orphanage. See this link which explains Constance's behaviour after the quest is completed. If you have indeed completed the quest, this is likely a glitch (maybe try waiting for 48 hours outside of Riften, and then returning, or reverting to a save game before the quest if possible). The glitch may involve her remaining in a state of panic, so she may be found walking around Riften. Another possible explanation is that she was possibly killed (for instance by vampires).
After doing some research on Honorfall Orphanage, I saw a piece of "Trivia", which says that Children can only be adopted if one has the Hearthfire DLC (in either case, the children cannot be adopted before Grelod's death).
Hope this helps.