Hope : S3 from Originals
So that she can meet Camille and Jackson and how she's going to deal with knowing that they are being killed but that she can probably change nothing. And that she meets Lucien, Aurora, etc.
Josie and Lizzie : S6 from Vampire Diaries
Same reason as for Hope. Just to see how they deal with knowing their birth mother is going to die but not being able to tell and doing nothing to stop it.
Alaric : S2 or S3 from Vampire Diaries
Because Alaric really hates Klaus and it would be interesting to see the Alaric of today fighting on the side of the Mikaelson (because he will do anything for Hope to be born so he will have to help Klaus break the curse for example and even let Jenna die so he can have his daughters with Jo) then that the Alaric of the past will just be confused to have to fight against himself.
The others I don't know.