Mission 4 (Arcadia City): At the base of the elevator tower near the controls where you save Adam. Mission 3 (Relic Interior): The left side of the starting point, close to the Pelican crash site. It can be found at the top left of the map. Mission 2 (Relic Approach): Enter the area through the Covenant shield with the supply crates. Mission 1 (Alpha Base): Just under the last bridge before you enter the rear gates of Alpha Base.
There are also other Black Boxes that are unlocked by winning on each Skirmish map and winning a Skirmish with each leader. Each Black Box will unlock new Halo History entries. Search the indicated locations to find the hidden Black Boxes.