http://www.amazon.com/gp/aw/d/B00AOCSFYC
I have this one. Works pretty well and feels sturdy. The cable splits from the charge port into the auxiliary/usb. Plus it fits with a case.
I picked up this case and abso-friggin-lutely love it. The phone's so slim, and this case doesn't bulk it up... I had two people ask me if I was going to get a case for my phone... then I told them it was ALREADY in a case!
http://www.amazon.com/gp/product/B00F423NQ2/ref=oh_details_o01_s00_i00?ie=UTF8&psc=1
I also picked up this car mount that I love. It's not specific to the Note 3 but is much nicer than most universal mounts I've found and the company also provides a car-dock app that amazingly ISN'T garbage! This car mount works whether your phone is in a case or not but isn't nearly as bulky as a lot of universal mounts.
http://www.amazon.com/gp/product/B00AOCSFYC/ref=oh_details_o02_s00_i01?ie=UTF8&psc=1
I use AutoGuard BlackBox as a dashcam app with this mount and the iBolt Dock'n Drive dock mode. It works great. I have the Dock'n Drive turn on Bluetooth only when I mount the car in the dock and it turns it off when I remove it from the dock as well. It's all around a very nice setup.
I have the iBolt prodock. It's capable of holding my Note 3 with or without the case. Once you plug in the phone it switches over to docking mode and iBolt has docking software that let's you choose what icon are on the screen plus the ability to automatically shut off wifi and turn on bluetooth. Here is a link to it at Amazon