Mariah Carey flies back Wednesday from a whirlwind European promotion of her Billboard No. 4 BUTTERFLY, just in time for a Manhattan party celebrating her December COSMOPOLITAN cover. She has more singles due, and this weekend she guests on Saturday Night Live. It's a good time for Carey, almost six months after her breakup with husband Tommy Mottola. Behind the glitter, this honey-voiced 27-year-old is most excited about her new rental town house in New York, with a basement that will become a giant closet. "You can't wear something more than a couple of times or they diss you in the magazines!" She's had the house a month. It's "so homey," she told me, probably a change from the up-state mansion she and Mottola built. This one has no recording studio, but it does have lots of fireplaces and a den that came decorated so that Carey can, if she wishes, watch TV before the fire, lolling in a mahogany upright bathtub--"all my favorite things." Nobody is joining her in the tub for now: She says she's not seeing anybody. "I have enough on my mind, and it's hard for me to know who's interested in me for me, and who's trying to get a little press." Her Cosmo advice about a separation: "Don't do the rebound thing, just try to understand how you can grow from the experience...I don't need to sleep with, like 100 guys to make up for lost time. If I'm with somebody, it's going to be because I really love him, not because I feel the need to go wild." She does have her pups to keep her company: Jack, the Jack Russell seen at the end of her "Honey" video, and Ginger, a Yorkie--"a boy and a girl who sleep in the same bed." She's focused right now on her continuing support for BUTTERFLY; she wants "My All" (good choice *the writer wrote that:)*) for her next single, and "Breakdown" is a strong cut getting a lot of radio play. Carey would like one small Cosmo clarification: The story says her family didn't have money to buy her shoes, but she says her mother would have if asked. Carey was about 18, on her own, and "I didn't want to ask anybody for anything." Carey is the third celeb to grace Cosmo's cover in the reign of new editor Bonnie Fuller (after Jennifer Anniston and Elizabeth Hurley). Fuller says Carey's a perfect Cosmo woman because of "her enthusiasm for life, she's a go-getter, directing her own career and her personal life. And she worked extremely hard, from modest roots, to fulfill her dreams."