Does it matter when you visit each major city? I am starting to use the carriage to hit each major city hub just to make fast traveling easier, is this a bad idea?

No, nothing bad will occur, but youll miss a bunch of stuff in the wilderness if you only fast travel.

I dont only fast travel, I just like to start at a major city and go out that way. I usually try to walk to my destination then fast travel to turn them in, get quests or when I need to sell my loot.

You should be fine then.