I'm most likely to use the remote when shooting tripod-mounted, so I've been meaning to use some velcro so that I can attach the remote to an upper tripod leg section. The band around the strap is a pretty good idea except that I usually remove the strap when I'm not shooting handheld (gotta love the quick-release connectors on the OpTech straps).
One thing I just found, that plastic pressure ring with the tools that is provided by the tripod manufacturer there a space to put the wire of the remote and after that tie the end of the remote with an elastic above that ring.
I use velcro for everything, including for the lens cap to stick to my camera back. If you place it on the ground, you're gonna walk away and forget it. Put velcro on your remote and it'll stay in place. The new velcros aren't that rough on the rough side.