Mission One: Valkyrion
Targets: Nascent Val'kyr and Valkyrion Aspirants.
These two mobs award very different loot, but respawn quickly. The Nascent Val'kyr fly around, and have a habit of descending on you from seemingly nowhere. They have a 100% drop rate for Dissolved Soul Essence, which sells to a vendor for 13.50g per stack! They also drop grays and miscellaneous greens, just like any other humanoid.
This mob is also the only mob in the game that will drop [Design: Fractured Scarlet Ruby], and patch 3.1 will be buffing Armor Penetration, so it may come into fashion. You have to be a Jewelcrafter to see this drop, and it is bind on pick-up, so the only profit to be had from it is through its use.
The Aspirants drop Frostweave Cloth 29% of the time (according to Wowhead), and Relics of Ulduar 41% of the time. The Relics can be sold for a high profit, usually in large stacks like 100, as they are turned in to the Sons of Hodir for reputation in stacks of 10. You will also end up picking up greens, grays, potions and scrolls.
Daily Tip: Once you've played through Brunnhildar Village, you can go there each day for a daily quest or two. Often, Gretta the Arbiter will give you the quest, The Aberrations Must Die, which will take you into Valkyrion to complete. You will get an extra 13g23s at level 80, plus a chance at the White Polar Bear Mount.
Mission Two: Fjorn's Anvil
Target: Seething Revenants.
These elementals will also drop Relics of Ulduar, although the drop rate is lower, set at around 33-34%. Their main draw is the Crystallized Fire, with about a 26% drop rate. Both of these items sell well on the Auction House, and you'll want to check your server to see if you should be selling the Crystallized Fire itself, or combining ten to form Eternal Fire and selling that.
Their most common junk drop is Hoary Crystals at 81% of the time, and a stack of 20 will sell to a vendor for 3g91s.
Daily Tip: Once you've unlocked the Sons of Hodir daily quests, you can go to Dun Niffelem to pick up the quest Hot and Cold from Fjorn's Anvil. Upon completion, you will get an extra 13g23s at level 80.
Mission Three: Frostfield Lake and Mission Two
Targets: Brittle Revenants, and the above Seething Revenants.
Because the daily quest, Hot and Cold, has you going to both locations, and because the area can be highly farmed at certain parts of the day, you might do better to do a circuit through the two adjacent areas.
Brittle Revenants are icy, and will drop everything that their fiery cousins drop, with the substitution of Crystallized Earth for Crystallized Fire. Earth is not in high demand, because it drops readily for miners, but depending on your profession, you could use them to make money. For example, Tailors can use it to craft blue PvP cloth gear, certain high-end, profitable epic jewelry take six Eternal Earths, and Enchant Gloves - Armsman and Enchant Shield - Defense use up an awful lot, and sell well.
Quick Gathering Tips:
The Plain of Echoes is filled with Rhinos (that romp!) and Mammoths, and so does The Foot Steppes.
The clouds in the area will drop Crystallized Air and Water.
Herbs are all over, and they aren't just along mountain bases. Once you have Cold Weather Flying, don't forget to search all the way up mountains. Both Icethorn and Lichbloom grow next to rocks and trees near rocks, so although there are some that can be found out in the open spaces, they are on rock outcrops.
If the province is crowded, take a trip across the southern slopes that fade into Zul'Drak. Nothing is there, except for herbs! I never find competition in that area.
Cobalt: There isn't much, and what the province does have is really on the border into Zul'Drak.
Saronite: This can be found all over the map, much like the herbs.
Click on either of the links to view maps. I strongly recommend getting an addon such as Gatherer to help you plot your farming excursions!
Dirkee can be found to the west of the Terrace of the Makers, facing Ulduar, or near the Engine of the Makers, or finally, between Camp Taunka'lo and Thunderfall.
Vyragosa is found just outside the Grommash Crash Site, on the side leading down into the Snowdrift Plains. She will drop a blue leather helm with a random enchantment.
Time-Lost Proto-Drake will drop a mount, Reins of the Time-Lost Prot-Drake! One commenter on Wowhead posted an excellent map showing where he spawns and how he paths.