As you could have guessed Ilum is the best place to farm Archaeology materials at max. The sheer amount of materials around this planet is amazing even with other people farming here with you. It takes roughly 15minutes a cycle and is very profitable, especially if you have Scavenging, Bioanalysis or Slicing too. I make roughly 10 to 15k a cycle from running around Ilum and that doesn't even include the profit I was making from missions at the same time.
This is the path that Imperials will be using to farm materials on Ilum. It's a bit like the Republic path but it goes through all of the Imperial "friendly" zones. The only area where the path cuts over into a Republic area is the blue line in the upper left. The reason I still recommend going up here is because there are a ton of materials for players up here as well as a large chest where it says "Chest" on the map. It's worth fighting your way through this area and at least collecting this chest if nothing else.
There is also a chest in the far northeastern end of the zone but you will need to run through some elites to get up here. Granted by the time you reach the chest they will "leash" you may get dismounted and owned while getting to here depending on what level mount training and mount you have. Aside from that chest there is another one which you will be running by near the Republic Outpost in the center of the zone. Once again this is another small chest and not a big one like what's in the far northwest where the blue line is.
The path you will be following through Ilum is as straight forward as can be, the only thing that may confuse you just a little bit is why the line suddenly gets bold. The only reason I did this is so you didn't confuse the lines when they kind of intersect. The bold path is the line you'll be following on the way BACK to the start point. That's about all you need to know for farming for all Gathering Crew Skills on Ilum (Except Slicing, that needs its own guide and map).
Damind Crystal - (10 a run, 1750 Credits)
Hypertech Artifact Fragment - (10 a run, 1100 Credits)
Alien Artifact Fragment - (7 a run, 900 Credits)
Upari Crystal - (10-20 a run, 2000 - 4000 Credits)
Blue Polychromic Crystal - (25 a run in total of color crystals, 4500 Credits)
Red Polychromic Crystal - (25 a run in total of color crystals, 4500 Credits)
Green Polychromic Crystal - (25 a run in total of color crystals, 4500 Credits)
Primeval Artifact Fragment - (25 a run in total of color crystals, 4500 Credits)