Where I'm coming from is as such. When you accept a visual approach it is still an IFR procedure regardless of the fact you're using your Mark III eyeballs to position yourself for a safe landing. You're not flying a precision or non precision approach, you flying a VISUAL approach usually with a vector towards the airfield. Once you're cleared for that approach you're pretty much on your own to make the field. There is no published missed approach and even published visuals rarely if ever have some procedure in the event of a go around (I've never seen one with a published missed) so it simply defaults to a climb on runway heading and a timely call to ATC. What else is there to do?
I don't believe entering the pattern without ATC telling you to do so is the correct way to go. You have no assurance of clearance from traffic and obstacles. Generally the patch directly on runway heading is the safest bet and most likely where ATC would expect you to be on the missed following a visual approach. I will try to find some sources to back my claims for you.
Edit:
Going through a United FOM I happen to have it quotes:
"A visual approach is
not an instrument approach procedure (IAP), and therefore
does not include a missed approach segment or procedure. If a go-around is required, further clearance or instructions are issued by ATC to ensure separation from other IFR airplanes."
So stand by my acsertation to remain on runway heading while climbing and advise ATC. In my experience ATC will generally vector you in way that resembles a traffic pattern and give you a base turn to final. Or bring you all way to the back of the sequence. Hopefully it's the former.
