You have the same card as me. The game was coded very poorly and wasn't properly designed to take advantage of PC hardware the way we're used to from modern Western games. It's a singlethreaded game - this is the reason why your CPU sees very little activity. It uses up RAM, but you have way more than what the game needs. The big issue with the game is that it tries to render every polygon of every single graphic model in Eorzea - it doesn't have.. I think it was LOD? textures (lower quality textures it can use from far away) to render people who aren't near you. The game has a crapton of polygons but it's not terribly efficient at them. Trees and foliage, as you noticed, are notorious for this. If you've ever tried to walk through the Christmas tree in your city, you'll know what I mean.

There's only three things you can really do to compensate for the poor optimization. Either buy an overkill GPU setup (dual SLI GTX 590's), wait for 2.0, where they promise to have a fully optimized-for-PC engine, or dial down your graphics settings so the game doesn't chug in foliage.

Oh, another thing to do, if you notice that it gets a bit jerky in town (like as though it's loading stuff), move FFXIV to an SSD. The game loads TONS of little files related to every single player character around you. This results in a lot of small read/writes (another example of how poorly optimized the game is). An SSD will mitigate these load stutters in town because of its fast random read speeds.