I read somewhere that if you wear heels during the day, you should run in the a.m. b/c heels tighten up your achilles and running at the end of the day could be problematic.
As my training load increases, I wear heels less often, not only for comfort but because I am clumsy and don’t want to injure myself.
But for a night out, the higher the better! I have a closet full of 3-4" heels that come out to play every so often. I just make sure to run (and shower) before I put them on…
The better quality the shoe, usually the more comfortable the heel, regardless of height. I buy a ton of shoes now from Zappos.com. Some really comfortable, but stylish brands they carry are BCBG, Casadei, Donna Karan, Anne Klein, Via Spiga, Donald Pliner, etc. The best customer service, selection and prices I’ve found online. And they carry handbags as well 
They are the “Amazon.com” of shoes.