A big +1 for Hawaii, but for Kauai and not Oahu. Kauai has much fewer residents, tourists, and crime. I've never felt unsafe there. I've been there three times by myself. (Granted, I am a guy, but I am also a frady-cat.)

Or if you want SECLUDED and almost nothing to do, go to Molokai. You can have the whole beach to yourself. It's not hard to find deserted beaches in Kauai, but you'll almost always have a rooster around. And the guide book I read last time, was quite comical about it... Saying something about the roosters in Kauai being particularly stupid, and because they don't know when to crow, they just do it all day and all night.