I’ve worn fanny packs for over 20 years. The StashSafe hip pack is the best one I’ve found. Specially-geared to prevent theft, the strap has stainless wire embedded inside so no one can cut the strap and run off with it. The buckle’s catch is hidden by a velcro-backed flap that ensures it’s neither visible nor reachable.
I used my pack heavily on a recent 6-week trip through Central America. The fanny pack is heavier and bulkier than many others (ed.: 300 grams). But it features several compartments and pockets inside that can carry a lot of stuff. In my case: two cameras, wallet, change, pen, small notebook, magnifying glass, penlight, swiss army knife, passport, watch.
You can also attach a lock between the two zippers and a stainless steel loop so they cannot be unzipped (pic below). I think this is more for locking it up when leaving it in a hotel room (and you can lock the bag around any pole or object that it can’t be slipped over). When I’m out and moving around, I go into it so often, it would be a drag to keep unlocking it, so I’ve never used a padlock.
Another item I bought from PacSafe, but never used it on my trip, was their backpack & bag protector, a stainless steel mesh web that fits over a backpack so you can lock it to some kind of non-movable post. None of my hotel rooms seemed that open to theft, but I’m sure in some parts of the world and in some neighborhoods, you might want added security (esp. with laptops, cameras, etc).