I pulled some resources together and created this list of all the known bag slot quests. I sorted them by region so you will have an idea of what to look for when you get into different places.
On top of that understand that you will get the Black Spirit quests that can be done anywhere. Please add comments if you find more. Also, I did some fact checking and added in all of the cities where you can find these NPC's.
https://docs.google.com/spreadsheets/d/1AciH0rlXRMelTjduu_NcY14d7nhz88anfHGUXJNcwzE/edit?usp=sharing
*Please don't mistake I didn't create this from scratch just realigned some information provided from other sites and sorted them based on region not level with color coding. I did however add a few cities other lists didn't provide.*