Head to the Botanists Guild in Gridania to become a botanist. Then, as you level your botanist your gathering log will automatically add the locations of items you can gather. Once you hit the level for elm logs to appear, go there and get them.

Same rule applies for any other thing botanist gathers

Oh, also, I highly recommend if you get into crafting to level all your DoL/DoH classes together. There's a LOT of overlap between them.