Though the Silmarillion is not specific about the awakening of the Dwarves, we can glimpse the reason why in the late essay Of Dwarves and Men (in The History of Middle-earth Volume 12, The Peoples of Middle-earth). Tolkien notes there that the Dwarves knew the details of their awakening, but kept them secret. It's logical, then, that the Elves who originated the Silmarillion couldn't have known where the Fathers of the Dwarves had awoken.
In the same essay, though, we are told where three of the seven Fathers awoke. The eldest and most famous of them, Durin the Deathless, awoke at Mount Gundabad in the northern Misty Mountains. Two more, the unnamed ancestors of the Firebeard and Broadbeam clans, were placed by Aulë in the Blue Mountains (and there presumably founded Nogrod and Belegost). The other Fathers awoke in pairs in two other locations, a thousand miles or more to the east of the Misty Mountains.