It's super important to find the Mjolnir Armory and Spartan Cores at every location on the map. However, at one of the first areas, The Tower, you'll struggle to find them if you're relying on your waypoints on the HUD. So, here's how to find the Mjolnir Armory and Spartan Cores at The Tower.
The Tower Interior Spartan Core
The first Spartan Core is easy enough to find. As you climb the interior of the tower, you'll be able to see it glowing in the corner of the third floor after you clear out a few baddies.
The Tower Exterior Spartan Core
This one is tricky to find. If you try to find it by setting a waypoint on your map, you'll fail and it'll take you to the very top of the building - pointless unless you're looking for the Skull.
In fact, this Spartan Core can be found on ground level outside of The Tower. Here's what you're looking for:
It's found in a small building tucked away in the corner underneath The Tower.
The Tower Mjolnir Armory
This is another tricky one to find. Your waypoint will send you to the top of the tower again, but this is also on ground level. Check the icon's location on the map and head towards the walkway going out in that direction, just past the Gravity Lift. Then, take a peek off the side.
The Mjolnir Armory is situated underneath that walkway on the cliff's edge. Here's what you're looking for:
That little green icon is flashing about the place, so all you need to do is go up to it and claim your reward. It's a rather nice multiplayer cosmetic, so all you need to do is customise your Spartan to take advantage of this.