I'm enjoying the game but dying a lot as I explore as there are some high level enemies around the starting town. Do I lose exp or currency or anything for dying?
There is no penalty at all for dying in Xenoblade Chronicles. If you die, you just go back to the last landmark you have been to before dying.
The only thing that you could consider as a penalty is that all the ennemies that you killed prior to dying reappear on the map.