Mugwort is a wild plant and can be found in a few places. One is on the road as you head up to the dig site, one can be found near the Artist's site and there are two on your farm (the easiest to find if you need them quickly.) Both can be found near the two fields that you have from the beginning of the game.
In the field next to your house, the Mugwort is just a little to the left of the tree behind the field I think.
On the field that is nearer the old shed, the Mugwort is to the right of the field, just by the tree which is directly behind the shed.
Hope that helped. ^_^