Assuming you have a shitty manager that doesn't respect "I'm not coming into work due to sickness. Using a PTO/NPTO day":
Food poisoning is a classic, people know it involves puking and shitting and fever, so they won't ask a lot of questions. "A crisis in the family"/"Personal crisis" is also good and vague, you can indicate something horrible has happened without having to explain in large detail due to it being "personal". You can also fake having a traffic accident/having your ride be fucked up somehow.

Regarding needing to be seen as good: Your work owes you sick days, the fact that it believes it doesn't is insane. You yourself decide when you are not well enough to go to work, and mental health is also health. If your workplace does not believe it's workers can get sick, then you should not believe it is owed an explanation. Furthermore: Most unions (where I'm from) that require sick-days also require that the boss cannot ask about the nature of the sickness as long as it is less than 3 days.