Prospector

Where to Mine Copper and Tin (Tier 1) 
 
The Shire offers good Tier 1 mining throughout the zone (except for Greenfields, that's tier 2). InBree-land, Chetwood and the Midgewater Marsh are solid choices. For elves and dwarves, mining in Ered Luin isn't very good. Consider a move to the Shire or Bree-land.
 
Where to Mine Barrow-iron and Silver (Tier 2)
 
In Bree-land, the Bree-fields and Barrow Downs are solid choices. Lone-lands and North Downsboth have tier 2 ore nodes in their western halves, but surrounded by higher level mobs. You'll get good mining in while leveling through these areas.
 
Where to Mine Rich Iron and Gold (Tier 3)
 
The Kingsfell area of the North Downs has great tier 3 ore node density. In Evendim, the Parth Anduil area between Tinnudir and Ost Forod is also node rich, but the mobs are a bit higher level. You'll find plenty of nodes in eastern Lone-lands while leveling there.
 
Where to Mine Dwarf-iron and Platinum (Tier 4)
 
For tier 4 ore nodes, western Trollshaws is quite good, starting just across the bridge from Lone-lands. The Ram Duath area of Angmar, just inside the zone from Esteldin is decent, but a small area. The west shore of the lake in Evendim is also good, especially with the fast boat route to cut down on travel time. Finally, tier 4 ore is all through western Angmar. You'll pick up plenty while leveling through Angmar.
 
Where to Mine Ancient Iron and Ancient Silver (Tier 5)
 
You can mine tier 5 ore at a lower level in Forochel, though the nodes can be pretty spread out. High Pass in Misty Mountains, has good density, but it's a trek to get there. Some miners set their milestone there and use a house or racial port to get back and forth to the AH. If you are high enough level, the best place for tier 5 ore is Eregion, especially around High Hollin and Echad Eregion.
 
Where to Mine Khazad-copper and Khazad-tin (Tier 6a)
 
Khazad-copper is in great demand now, so expect a lot of competition when mining for it. The best place for Khazad-copper and Khazad-tin is the Nan Sirannon area of Eregion, both north and south of the river. The Durin's Crossing area of Durin's Way can be good during off hours. Silvertine Lodes and Redhorn Lodes also have Khazad-copper, but the nodes are more spread out.
 
Where to Mine Khazad-iron and Khazad-gold (Tier 6b)
 
Khazad-iron and Khazad-gold are plentiful in the Golden Wood area of Lothlorien and in Mirkwood. Although khazad-iron and khazad-gold don't sell that well, many people mine it with hopes of getting a mithril flake. Worth trying when leveling in these areas.