"the first places" is correct and usable in written English.
You can use it when referring to a list of items ranked in order. For example: "The first places for the marathon went to Mary, Susan, and Kyle."
Cambodia was one of the first places I visited abroad.
"You may think you're being clever, but these are the first places burglars look".
Cities are also the first places to feel the results of the migration from conflict zones.
One of the first places I visited was a home called Platinum Body Logic.
Her shop is one of the first places I go when I'm in Paris.
But one of the first places to look is Charlotte's public-school system.
They arrived last night and claimed one of the first places in line at 10 p.m.
It is the first places to successfully breed threatened crimson-faced bald uakaris in captivity.
Whenever there's a slowdown, he said, those are the first places to get hit.
The measures would create the first places in the UK where smoking outdoors is banned.
Spain and Scotland became the first places outside North America to confirm cases.
