On the bike, I usually put it in my jersey pocket, bento box, or camelbak (though sometimes the camelbak seems to get worse reception, maybe because my cell phone is in there too). Wearing it on my arm doesn't really bother me, either, but it's nice to have other places to put it. For the bike, I mostly use it to measure my route and how heart rate and speed and distance line up, I use my bike computer to show me current speed and distance.
When I'm running, I put it in my shorts pocket, or on my arm if I've got long sleeves on (I don't need another seam to chafe against with short sleeves). For running, I use it to measure everything.