When you reach level 41 I recommend doing the quests in Red Mane Cavern. Needless to say there are quite a few quests here. It will be a little bit overwhelming at first but I'll break it down to help you get them all done quickly. When you first get here turn in any pending quests you have. Then grab all the quests in town that are available to you.
Don't forget to accept the quests from Thor and his cronies all the way up top, these quests are easily miss able. Also don't forget to "refresh" all quests in town, this means if you have a quest that requires you to speak with someone else in town, do so. Before leaving town make sure you have the following quests:
Like I said, an overwhelming amount of quests. The first pair of quests you will want to do are "Freyja's Desire" and "Mamut's Bones". The area you will want to go to for the quests is southwest of Red Mane Cavern, Mamut Graveyard.
Kill 11 Snowy Mamut
Kill 7 Snowy Mamut Calfs
This quest requires you to kill the local residents of Mamut Graveyard, the Mamut Calfs and regular Mamuts. If it is nighttime the Spirit versions of these Mamut's will be out and you won't be able to complete this quest. I recommend grinding during the night or doing the "Summoning Phagrasul" quest.
Collect 7 Mamut Bones
This quest requires you to collect 7 Mamut Bones, go figure. Each of these bones can be found on the ground, as seen in the picture above.
IMPORTANT NOTE: At night a level 43 Elite Mammoth walks around Mamut Graveyard. He has a HUGE agro range and will kill you. Also at night all the Mamuts will despawn and turn into Mamut ghosts. If you come here at night or it turns night while you're here I recommend just grinding until day. Also if you have the "Summoning Phagrasul" quest you can do that at night.
Towards the back end of the Mamut Graveyard you will also find the large Mamut Skull. You will need to interact with this skull in order to summon the soul of the Gigantic Phagrasul. Below is a picture of the skull you will need to interact with as well its location on the map.
Gigantic Phagrasul will appear when you interact with the skull, speak with him and refresh your quest. Now you will need to kill 5 Mamut Souls and 5 Mamut Calf Spirits. These two mobs only appear at night.
After you finish these three quests you will want to return to town and turn all three of them in. Now you will want to head east out of town to our next questing area. You'll want to do the "Decorative Skulls" quest first. It requires you to kill Rynoce's for their skulls.
The best place for the Rynoce's is my blue circle on the map, however you can find them all over the snowfield to the east. After you're done you will want to head back to the camp of Fang Trolls that you where killing at level 40. If you forget where they are or you never killed them take a look at my map below.
The troll houses are pretty noticeable, in order to destroy the house you will need to kill the trolls standing outside then the troll inside. After you've done that you can destroy the house from the inside. You will need to do this to 5 different Troll Houses. After you've completed both quests return to town and turn both of them in. Accept the follow up for the Troll quest.
Now from town you will want to head in the same direction as the Mamut Graveyard, but this time to the Harpies. If you've never been to the harpies before, or forget where they are take a look at my map below.
The line is where you can find Carpen, they are fish in a lake that require Extract Vitality Skill of 345. You will want to gather 12 of these. You can find the Virago Trackers and Tundra Hunters in this area as well. They are the Harpies that are here, they are usually over camped, so this may be a tad bit of a pita to do. While you're here killing the harpies be sure to collect 15 Subella for your "Drinking for Two" quest.
After you kill all the Harpies you need and collected all the Carpen you will want to continue a bit east to our next area. The next area you need to go to is the island just east of Beluslan's Roof. Here you will need to kill the Ice Canyon Griffo's for 5 Griffo Down and 7 Griffon Feathers.
The Griffo Down drops from the small Griffo's that look like mini Chocobo's and the Griffo Feathers drop from the large Griffons. Below is pictures of both of the Griffo's that you will need to kill for your quest.
After you complete your quests you will want to glide down into Frost Spirit Valley. Here you will want to carefully dodge all the mobs and collect 7 Tear Crystals. These Crystals can be found all over the ground down here. Use your quest tracker to find them if you have trouble seeing them.
After you complete this quest you will want to return to town and turn in all of your quests. Accept the follow up quest "Feast Fit for a Skurv". For this quest you will need to return to the same area you killed the harpies but kill the Fierce Daru and Crookhorn Gorgon's for 2 Gorgon Rib Chop and 3 Daru Hock Meat. Gorgon and Daru Locations for farming up Gorgo Rib Chops and Daru Hock Meat.
After you complete your quest you will want to return to town and turn in your quest. Accept the follow up then speak with Baba Kun to turn in your quest. After you turn in your quest you will want to fly to Besfer Refugee Camp and turn in your quest here. When you're done fly back to Red Mane Cavern and head east to the Fang Troll Encampment.
You can grind out your "Eradication Pa-Troll" quest in one of 3 areas. Fang Troll Encampment area recommendations for level 41. At one of these areas you will need to kill 20 Fang Troll Hunters and 30 Trollkin Warriors. Once you're done your quest return to town and turn it in. Hey look, what do ya know it is a repeatable quest! =P
Now, you have the option of continually repeating this quest to level up or to grind in one of the other areas... Hint hint, the balaur area! =D