Don't drill the bottom, under the U shaped bottom cover is the mic and the antenna. I wouldn't suggest the side rails or the battery cover either - they would pull off too easy IMO.
Best suggestion I can think of is to drill two small holes close to the speakerphone "outlets" on the top of the phone that you can loop a lanyard through.
There's a couple mm of space in there to work with. You'll need a T5 screwdriver to open the phone and a T6 screwdriver to remove the main board from the internal support to be able to drill safely.
Some poor images of the area I'm talking about :