Ok. Let me clarify.
VFR arrival to a towered airport:
Fly straight ahead, request closed traffic:
"Citation 1234, going around, request closed traffic"
Cleared Visual Approach (day or night):
Fly straight ahead to predetermined altitude or as instructed by ATC. I usually plan 3000' agl or the normal altitude that ATC clears me to when I depart the airport. If I can't fly straight ahead due to whatever (terrain, weather, etc), I'm going to notify the tower before turning.
"Citation 1234, going around, unable runway heading, request right turnout."
Cleared for the ILS (regardless of the weather conditions):
Fly the published missed approach or as instructed by ATC.
"Citation 1234, missed approach."
With any of those situations, tower IS going to give you instructions. The reason that I personally brief, is so that I have something in mind in the unlikely event that all of a sudden I lose comms right as I hit the TOGA button.
VFR arrival to a nontowered airport:
Set max thrust, pitch for 45 degrees and roll 180 degrees simultanously, then pull through vertical to line up for an opposite direction arrival.
"XYZ airport traffic, Citation 1234, going around from runway 6- we'll be executing an overhead half cuban eight for an opposite direction arrival to runway 24, full stop, XYZ airport."
Last scenario aside, what you do is EXERCISE common sense and your authority as a PIC to ensure the safe outcome of your flight. Fly like you brief and brief like you train.