Fame, money, women – you’d think it would be all a rocker needs to get by, but for Lenny Kravitz, it’s just too much. The musician – whose every hair style and clothes change is snapped by the paparazzi – sings “I Don’t Want to Be a Star” on his new album, Baptism. “You miss the way it was before people were, like, hunting you,” he says. But still, there are perks to being a big celeb. Kravitz (who’s dad to Zoe, 15, with ex Lisa Bonet) recently chatted with PEOPLE about some of the pluses – including dating Nicole Kidman and living next door to Courtney Love.