You bought MHP 2nd for its many exciting and adrenaline-filled quests, okay maybe not those transporting quests but compare to MHP, MHP 2nd has plenty more to do and kill. I am by no means a pro in killing these monsters but here's a rough guide to quests that I have been through.
1. 雪山草摘み
Collect 5 Snow Mountain Herbs and send them to the red color supply box at your base. They are those little plants in the snowy part of the map (area 6, 7 and 8).
2. 雪の山のガウシカ
Kill those wild goats (Gaushika) in order to get their horns. However, not all of them contain ガウッカの角, so you just need to kill lots of them until you get three.
3. 肉食竜の討伐
Kill five of those annoying ギアノス (W Velociprey), there are exactly five in the map.
4. 忍び寄る気配
Send three ポポノタン to the supply box. This mission is the first at night and is the first time that 轟竜ティガレックス (Tigarex), the star of the game appears. For ポポノタン, you have to kill those wild elephants with big horns (Popo). You'll find them in area 6, but they will run for their life to area 7 as 轟竜ティガレックス landed in 6. So run to area 7 and kill them. There are more of them in area 8, where 轟竜ティガレックス will comes if you stay too long.
5. ブランゴを倒せ
Go to area 8 and kill three of those white monkeys (Brango).
肉食竜のリーダー (Emergency Quest)
This quest will pops up once the above five are completed. I see this as a more powerful version of the ギアノス (W Velociprey) in Quest 3 above, called ドスギアノス (Dosgianos) and much cleverer than it was in MHP. It can now hurt you while you are slashing him, so unless you know what you are doing, just avoid attacking it straight on. I find attacking it from the side is the best way, and it has small movement areas as well, they are 6, 7 and when it is weak, 8. Get this quest done and the Village ★★ Quests will be available.
Click here for Village ★★ Quests