Nike Expandable Lean WaistPack
Let's face it. Unless your arms are the size of Dwayne Johnson's, a running armband for the Note 3 (they do exist) looks ridiculous. For the runners out there, do check out running belts like SPIbelt (tight fit for the Note 3) or the cheaper Nike running waistpack pictured below, which works just as well.
Running belts do a good job of housing your phone and keys, while eliminating bounce. Just remember to place your phone in a plastic bag if you're heading out in wet conditions to avoid water damage. Pair your gear up with an exercise bluetooth earphones (
Bluebuds X recommended) and you're good to go. Control volume and skip tracks from the earphones itself.
Too heavy? Run light but still with your music and distance logged using this.
Pictured: iPod Nano 6G, LunaTik Wrist Strap, Kokkia i10s Bluetooth iPod Transmitter