If you don't want to call it a fanny pack, you can also call it a belt bag. I have several of the Everyday Belt Bags from Lululemon. They are only $38, and have one zippered pocket on the part next to your body (the outside part but the back of it), and three mesh pockets inside (two small, one large enough to fit a phone) and the main zippered compartment. I can fit my small wallet, key, cell phone, my Ray Bans in their case, and a small tub of lip balm and hand sani.
I agree with above I do not like wearing the fanny packs like a cross body, esp since I have a bigger bust. If you buy a fanny pack, wear it as a fanny pack, or just get a cross body. It's ok to like something that you once thought was unhip. I grew up in the 80s. We were all over the nylon bright color fanny packs. The ones today are much more sleek. Unless of course you want to wear that kind to be ironic.