There isn't a lot we can say for certain about the ending of the novel, but isn't that what makes it worth thinking about? We do know that Holly has ended up in Argentina (at least according to her postcard), we know that the narrator is finally able to locate Holly's cat, and we know that he wishes good things for Holly in the end. But what we don't know for sure is if we're left with a happy ending or if Holly's life is just going to continue to be as crazy and as chaotic as it has been for the rest of the novel. After all, we as readers may find the story of her life interesting and a little exotic since it's probably so unlike our own lives. But at some point it becomes pretty clear that Holly's life scares her a little bit, and if we like her at all this might make us feel bad for her. So it's hard to know what to make of the ending, but this is OK since this allows us to come up with our own interpretations.
On the one hand, Holly seems like she's found happiness in Buenos Aires. She's escaped going to jail for being associated with Sally Tomato, she's fallen in love with a "duhvine $enor" (19.1) as she tells us in her postcard to the narrator (we're guessing the "$" in his name means he's divine and divinely rich), and she seems to be living the same kind of exciting life she had in New York. So, this all sounds pretty good for her, and this is certainly one of the many ways we can interpret the ending.
But it's also possible that the ending is not as happy as it seems. Holly also tells us that the man she's fallen in love with is married and has kids, and that she has no place to live because she can't live with him. So she's ended up with yet another unavailable man and is still moving around, not really belonging anywhere, as a result. And when the narrator tells us that he never hears from Holly after this postcard, we're left to wonder what actually happens to her. Maybe she's blissfully happy for the rest of her life, but maybe she's still scared of never finding a place to call her own, never forging long-lasting, meaningful relationships with anyone, and never feeling settled. We don't really know what happens to Holly Golightly, so we're left wondering with the narrator if she ever finds a place where she belongs.
This open-endedness might bug some of us since it's often easier to deal with a text that actually provides some clear closure to the events in the novel, and Breakfast at Tiffany's doesn't do this. But we think the texts that don't sum everything up for us cab be even more fun since we get the chance to create a little meaning ourselves. Regardless of your stance there, the open ending is pretty cool in that it reflects Holly's character in a lot of ways. Holly is all over the place and is hard to read and difficult to understand, but something in the narrator and in readers wants to keep trying. The ending of the novel is kind of the same. Plus, Capote does something pretty cool by creating a circular structure with the ending that links back to the beginning of the novel. Remember that Joe and the narrator don't know where Holly is or what she's been up to when we first start reading, and even after all we go through with her throughout the course of the novel, we still don't know where she is or what she's up to by the end. In this way, the open-ended conclusion seems kind of perfect.