Alliance

Best starter zone for Herbalism is Dun Morogh. Why? Most dwarfs/gnomes go mining.

Very little competition for the herbs.
Start with Peacebloom(grass) and Silverleaf(trees) in and around Kharanos. By the time you are high enough level (7+) to go to Brewhall village, your skill should be 25+, and you can start gathering Earthroot (hilly areas).

Aim to have 60-70 skill in Herbalism before moving to the next area.

Secondary areas:
Loch Modan or Westfalls.
I prefer Westfalls. The mobs are not as tihtly packed as Loch Modan.
Here you want to start with Briarthorn(Trees) and Mageroyal(Open gress/sand areas) to get your skill to 100+ before you can harvest Bruiseweed(Near buildings/bridges).
Aim to get your skill to 125+ atleast.
You can also try Redridge, but the Horde frequents the area too often.

Third areas:
Tough choice between Wetlands or Hillsbrad Foothills. Both have Liferoot which will give you the majority of your skill-ups. Look along the water-edges.
Other option is Duskwood for skilling up on the Ghostweed. (Forgot exact name).
This should get you to the 180+ skill

Next is Hinterlands & Arathi Highlands. Also STV.
Hunt Sungrass & Khadgar's Whiskers. It will boost your skill to the 230-240 range.

2nd to last area is Desolace.
In the southern area is Gromsblood. Guarded by relatively low level mobs for the herb. Should get you to 260-270.

Final areas is the Crater, Tanaris, Felwood and Winterspring.
The final bunch of herbs should right here to get you to 300.