• UC Distribution center
• Offworld Outfitters
• Centurian Arsenal
• Trade Authority (it's in The Well, which you can access from the elevator to your left when you enter the train station at MAST; if you haven't done any quests that take you here, you may not even know there like an entire second city underground)

All I can remember the names of; there's another gun store somewhere in the residential area that doesn't look like it would even be a store, and probably something I am forgetting about down in the Well.

Honestly, I don't like New Atlantis because the shops are so spread around and it has the oddest city layout I've ever seen. I get so lost here all the damn time, I prefer to shop in Neon. Everything important is on one strip, which the fast travel marker takes you right to the center of.