All information on where items are found is taken from
http://forum.square-enix.com/ffxiv/threads/43599?p=660467#post660467

All information on sweet spots, etc. are taken from www.mooglebox.com

To fully understand some terms and whatnot used here, take a look at this.
http://mooglebox.com/gathering/index.php

I have personally tested enough of these items to be confident that at least a majority of this is accurate.

LA NOSCEA
BEARDED ROCK, GRADE 1

These nodes are best quarried from by Miners level 1+
All-purpose Red Dye, yields 1
Ragstone, yields 1-3

LA NOSCEA
SKULL VALLEY, GRADE 2

These nodes are best quarried from by Miners level 8+
All-purpose Red Dye, yields 1
Ragstone, yields 1-3

LA NOSCEA
BLOODSHORE, GRADE 3

These nodes are best quarried from by Miners level 18+
All-purpose Red Dye, yields 1
Ragstone, yields 1-3
Water Rock, yields 1
Wind Rock, yields 1

LA NOSCEA
CEDARWOOD, GRADE 4

These nodes are best quarried from by Miners level 28+
Water Rock, yields 1
Wind Rock, yields 1
All-purpose Red Dye, yields 1

LA NOSCEA
IRON LAKE, GRADE 5

These nodes are best quarried from by Miners level 38+
Water Rock, yields 1
Wind Rock, yields 1
All-purpose Red Dye, yields 1

THANALAN
BLACK BRUSH, GRADE 1

These nodes are best quarried from by Miners level 1+
All-purpose Yellow Dye, yields 1
Obsidian, yields 1-3

THANALAN
DRYBONE, GRADE 2

These nodes are best quarried from by Miners level 8+
All-purpose Yellow Dye, yields 1
Obsidian, yields 1-3

THANALAN
HORIZON, GRADE 3

These nodes are best quarried from by Miners level 18+
All-purpose Yellow Dye, yields 1
Fire Rock, yields 1
Lightning Rock, yields 1
Mudstone, yields 1-3

THANALAN
NOPHICA'S WELLS, GRADE 4

These nodes are best quarried from by Miners level 28+
All-purpose Yellow Dye, yields 1
Fire Rock, yields 1
Lightning Rock, yields 1
Mudstone, yields 1-3

THANALAN
HALATALI, GRADE 5

These nodes are best quarried from by Miners level 38+
All-purpose Yellow Dye, yields 1
Fire Rock, yields 1
Lightning Rock, yields 1

BLACK SHROUD
BENTBRANCH, GRADE 1

These nodes are best quarried from by Miners level 1+
All-purpose White Dye, yields 1
Obsidian, yields 1-3

BLACK SHROUD
EMERALD MOSS, GRADE 2

These nodes are best quarried from by Miners level 8+
All-purpose White Dye, yields 1
Obsidian, yields 1-3

BLACK SHROUD
TRANQUIL, GRADE 3

These nodes are best quarried from by Miners level 18+
All-purpose White Dye, yields 1
Obsidian, yields 1-3
Earth Rock, yields 1
Ice Rock, yields 1

BLACK SHROUD
HUMBLEHEARTH, GRADE 4

These nodes are best quarried from by Miners level 28+
Earth Rock, yields 1
Ice Rock, yields 1
All-purpose White Dye, yields 1
Silstone, yields 1-3

BLACK SHROUD
TREESPEAK, GRADE 5

These nodes are best quarried from by Miners level 38+
Earth Rock, yields 1
Ice Rock, yields 1
All-purpose White Dye, yields 1

COERTHAS
GLORY, GRADE 4

These nodes are best quarried from by Miners level 28+
Mudstone, yields 1-3
Siltstone, yields 1-3
Wyvern Obsidian, yields 1

COERTHAS
DRAGONHEAD, GRADE 5

These nodes are best quarried from by Miners level 38+
Siltstone, yields 1-3
Wyvern Obsidian, yields 1
Astral Rock, yields 1