Suggest Level to About 30+ and Go to stranglethorn vale, 80% of Stranglethorn Vale are Beasts, and They are level 31-38, but can be up to 43 (max). STV is skinners heaven and there are many quests to get you levels. I started at level 33 and i am now level 39 and there are many quests to go for me. I've grown just over 100 skinning levels there and i also caught my pet there. I suggest hanging around Nessingwary's expedition( NW Near Westfall) and just Skin away, You can get med,heavy and thick leather there and also shadowcat hide from shadowmaw panthers( lvl 34+). There are also quests for your there. And After your bag is full, There is a vendor in the Rebel Camp and You could go back to booty bay by flying from westfall or walking ( Long walk ). Hope i Helped.
Though if you are horde, go to grom'gol.
Though for a current level 24, i would suggest wetlands, or ashenvale.