Is Lilo and Stitch set in a real city?
No.
In some ways it reminds me of the northern side of Koloa, but the shops are closer to what you see in Kapaa.
You are definitely on point there, per: ‘Lilo And Stitch’ Find A Home In Hanapepe
Those familiar with the island recognize that the setting seems to be a blend of Kauai’s North and Southeast shores.
is it just a made-up composite of multiple places?
Yes, but the town which inspired the setting for the film was Hanapēpē in Kaua`i County, Hawai`i.
From: Kauai town inspired Disney's "Lilo & Stitch"
“In the small town of Hanapepe, I found all the usual homey details, ranging from rusted-out bridges to homemade mailboxes,” wrote Paul Felix, the film’s production designer, in the official Disney “making of” book on the movie.
Do we know if their town is identified, officially?
From: https://en.wikipedia.org/wiki/Hanapepe,_Hawaii
[Hanapēpē] was the inspiration for Kokaua Town, the fictional hometown of the main characters in the Disney animated film Lilo & Stitch and its related franchise (the town was not named until Lilo & Stitch: The Series).

