I love Celephaïs. It's always this story in the cycle in which, for me, the Dreamlands start to take shape. The story reveals a permanence to the world of Dream which is independent from the conscious thought of the dreamer. Another point which becomes important later in the cycle is the fact that the Dreamlands experiences a different passage of time. Indeed, ones experience of time in the Dreamlands can vary wildly depending on their locale. We saw this also in The White Ship; the lighthouse keeper spent many aeons in the lands of Sona-Nyl, where there is neither time nor space.
Celephaïs is also a very tragic story. Though often Lovecraft's characters are nameless, something particular struck me about Kuranes' dream-name being revealed in the first sentence while we never learn his name in the waking world. Kuranes drives himself to ruin in the waking world in order to experience longer visits to his dream city of Celephaïs. Ultimately, Kuranes makes a permanent journey to the Dreamlands. In the waking world the unnamed broken body of a "tramp" is abused by the sea, a stones throw from Kuranes' ancestral home.