I have a little kidney shaped bag by Ameribag. It will hold my little camera, cell phone, I.D., lip gloss, and sunglasses. You can wear it across your body or tighten it up and wear it around your waist. It doesn't look like a fanny pack, but you can wear it that way. I usually wear it like a handbag across my body. It is called a the baglett. You can buy it in black leather or just about any color of microfiber. I have the a pink one. The nice thing about the microfiber is, I can just throw it in the washing machine.
You can check out what it looks like on Ameribag's website.