Most of these quest are not time-sensitive so you can go back to it at any time once it's been triggered. They are not chapter specific either and can usually be started at any time provided that the prerequisite sidequest has been completed.
This list simply gives the earliest possible timeframe a particular quest is made accessible to you. The game however does become quite linear in later chapters, so it's best to finish as much of these quests as you can when you still have the opportunity to explore freely.
Lestallum
The Cursed Canvas - 5000 EXP, 25000 Gil
This is a mission from Vyv after you complete "The Pen is Mightier than the Sword". And while you start this in the earlier chapters, you will not be able to complete it until chapter 9. Talk to Weskham after the story bits in his bar have ended then accept the level 32 hunt, "A Lost Painting". Mark the location on your map and go there to face Chadarnook. Defeat it and report back to Weskham before checking in with Vyv to finish up.
Altissia
Symbol of the Peace - 1000 EXP
Upon gaining entry into Accordio at the beginning of chapter 9, head north until you reach the first set of stairs. The party overhears conversation about Luna's wedding dress being on display somewhere. To find the shop, go up the stairs where you first heard about the exhibit and continue north passed the accessory shop. Ignore the stairs that you see up ahead and take a right passed it instead. Go forward and keep going up all the stairs until you get to a point where you can go down some steps to your right. The Vivienne Westwood is at the bottom of these steps.
Photo Op: Palace - 400 EXP
Head north from the docks and take a right up the stairs passed the accessory shop. Once you get to the top where the fountain is, countinue passed it and Prompto should ask about taking a photo of the scenery. Locate the photo spot and take a picture to complete this quest.