You could do the tech stuff in metric but the personal stuff in imperial.
Height measurement and weight of a person, body and room temperature should be in imperial, or the imperial numbers / units mentioned, those are not intuitive, and if you want to set things like a person is short and overweight by stating the numbers you will need to go imperial.
Travel distances such as walking, car travel, or like modes is better in miles, but KM also works. Elevation (above sea level, or accent of a mountain M can work, but feet may be better for the US. Spaceship travel in KM is fine.
If you chose to go metric, there are several ways to do it, like the person was brought up in metric from an immigrant or foreign family, from another country, or they have a passion for it they got from a school teacher in 7th grade, or their used car has it as it was bought from Canada, or a grey market new car. If you do, perhaps the reader can explain the conversion when it matters. If they live in another country altogether that is also a good reason for it. If they are metric by country, you can slip in the opposite, that they are interested in the imperial measurements and will put in both as part of the thought process, or even they are trying to learn imperial so explain the thoughts that go through their mind, or have a friend character who they will translate for understanding.
Another option is to use an archaic unit, or make up one if it’s a future setting or steampunk.
I don’t see the dilemma. If a story takes place in Asia and someone talks about a “journey of a thousand li”, or in England and a sailor mentions a depth of fifty fathoms, then it would be bad writing to change the text to explain anything or to convert what the person said to a different unit or insert a forced analogy or a gratuitous adjective or a footnote. If the reader was not familiar with such units before then she will be after getting into the story.
Neither is best. If it is fiction it will be boring if you use numbers. A person is tall, short or average. Water is shallow or deep or really deep etc. Sciency stuff you can use metric for but unless you are writing for a hard core tech audience you should explain plot points in terms people can understand. If something explodes at a set temperature you need to say it explodes at that temp and it won’t matter what system you use.
If the characters are Asian and use metric then use metric. They use minutes and hours just like everyone else so you can describe distances by travel time. Use other descriptive information along with metric measurements, so you can describe a character “He was two meters tall, noticeably taller than other men.” You can skip specific temperatures altogether for the weather altogether, just use word like “sweltering” and “freezing”. If you’re clever enough you can leave find a way to describe everything without a specific system or measurement.
The Star Trek Writer’s Guide dealt with this. “The weaponry control officers of a modern-day naval vessel will always be very precise in giving orders, but might remark conversationally to the man next to them ‘They’re still a mile out of range.’”
Metric. It’s no different than when I encounter unfamiliar units in other books like sci fi or 19th century novels. It’s clear from context that when Scrooge says he will give the little boy half a crown if gets the prize turkey that it’s a lot of money.
