Tools are necessary to upgrade your weapons and to unlock the "For Emergencies Only" trophy once you upgrade every weapon. The tools have fixed locations and must be picked up in the correct order during one playthrough. They do carry over to a New Game +. Note that getting them through chapter select will not help with the upgrades or trophy:
TOOL / CHAPTER
1. Chapter 4- Bill's Town- Graveyard
Inside the cellar (first floor) of the church is a hidden armory, and Bill will give you the nail bomb. Look in the corner with the metal shelf to find the toolbox.
2. Chapter 5- Pittsburg- Alone And Forsaken
After defeating the first group of enemies in the chapter, Joel and Ellie will enter a garage by helping each other through the shutter. Immediately after entering the garage, the toolbox will be on your left, next to the smoke bomb.
3. Chapter 6- The Suburb- Sewers
After reaching the opposite side of the flooded area with the generator, follow the path. To the left will be a room with the toolbox.
4. Chapter 8- The University- Science Building
After entering the science building by moving the dumpster, you will be in a room adjacent to a lab with a workbench inside. The next laboratory leads out to where you will meet back up with Ellie. You will then reach a long hallway. At the end of the hall is a locked door on the right. Open it using a shiv to find the toolbox on the work table.
5. Chapter 10- Bus Depot- Highway Exit
When you enter the Triage area with all the tents, go to the large tent on the left side of this area. Enter the largest tent to find the toolbox on the right.