Route A or Route B
11B's Memento - 5000G, Melee Defense Up, Ranged Defense Up, Melee Defense +6 Chip
I started this quest after completing chapter 3 but it can probably be done earlier. Visit the Bunker's hangar to meet 16D who asks you about the fate of her instructor 11B. After learning what happened, she then asks 2B to go to the abandoned factory and to see if she can recover any of 11B's belongings. Head the area where you first fought the buzzsaw arm of the Goliath machine during the prologue chapter, to find 11B's body.
Also, at the top of the stairs next to the access point at the factory entrance is the Virtuous Treaty weapon. Don't forget to claim that while you're here. Retrieve what you can from 11B then report back to 16D in the Bunker. She'll give you the YorHa-Issue Blade, tell her of 11B's escape plan as well to officially complete the quest.
Improving Communications - 320 EXP, 3000G, 5x Simple Gadget, 3x Medium Recovery
I started this quest after completing chapter 3 but it can probably be done earlier. Talk to the Commander in the server room and you'll be asked to obtain some materials so the engineers can work on upgrading the Bunker to Surface network. You need a Rusty Bolt, a Small Gear and a Spring. You should already have all of these on hand if you've been regularly destroying small enemies. Give them to Anemone at the Resistance Camp.
YoRHA Betrayers - 400 EXP, 10,000G
After reporting your findings on the alien ship to command at the start of chapter 5, check the access point in the Bunker and you'll find a new e-mail fro Operator 6O. Read it then return to the surface to receive more details on the mission. There are three hotspots around the city ruins and you need to check these locations for the supposed deserters.
The first encounter will be against 64B and 22B. Damage them enough and they'll retreat. Check the two remaining hotspots until you meet them again. You actually get to defeat them this time. With 64B and 22B dead, 8B will show up to fight. Defeat her too and you'll get to keep her Type-40 Lance weapon as well. That should be it for this quest.
Route B
Data Analysis Freak - 1,150 EXP, 3,000G, 3x Tech Manual, 2x Medium Recovery
After returning to the Bunker to give your report on the aliens, head to the administration room and speak with Operator 21O. She asks your help in transferring data to the Bunker from a terminal in the Abandoned Factory.
Go to the designated location and examine the data terminal by the wall, before heading to an area in the factory that has a good enough reception to send the data to Operator 21O.
Data Analysis Freak 2 - 5000G, 4x Black Pearl, Pod Program: A110 Slow, Type-40 Blade
After completing Data Analysis Freak, fast travel to the Resistance Camp and go outside. You will receive a call from your operator about this quest without being given the option to turn it down. Anyway, go read the email then head to the Desert Housing Complex to pick up these items: a Broken Toy, an Accounting Book and a pair of Kids Shoes. Go to an access point and claim your reward to complete the quest.