At the entrance to the mines

[Cúdae]

To add to what someone already said about the Elves and the Dwarves being friendly at that time, the road going up to the Western door (was it western... I think so. heh heh), was from Hollin--where the Elves lived. Besides that, the doors usually stood open with sentries watching them just in case.
The Dwarves told no one their language and they did not write it on anything that might be seen by another race. So, logically, if the Dwarves would not tell their language and the Elves and Dwarves were friends, the writing on the door would be in the language of the Elves. Did what I just type make any sense? Heh heh... I lose myself sometimes.