Anya owned (or leased?) a studio apartment in Sunnydale. There's zero indication how she came by it, but we can reasonably assume that it was created magically as part of her Anya Emerson persona.
We see it in several episodes. The episode script for The Replacement describes it as below;
INT. ANYA'S APARTMENT - THE SAME TIME - NIGHT
Only a tiny glimpse of Anya's apartment, a corner with a short cabinet
with an answering machine on it, and a few ancient Eastern ornaments
on the wall. Anya stands next to the answering machine, listening as
Xander leaves the message.
Buffy: The Replacement
And we see it again in Buffy: Selfless
INT. ANYA'S APARTMENT - DAY
Anya and HALLIE are sitting on the couch. Anya has changed out of her
You may find it interesting that whenever the script talks about her apartment, the script specifically calls for the set designers not to make up a full set, just corners and edges.