"Basin City" is set in an unspecified, fictional city in the American west according to various sources.
Though he has never said it's based on a particular city, given Frank Miller's love of noir (Hollywood influence) and the genesis of the comic during the "gritty" 1990s while he was living in Los Angeles, it's likely that Los Angeles was the model. Los Angeles is partially a basin city. The comic later establishes Sin City's waterfront as being very large, almost coastal in size.
The movie version of Sin City (2005) includes an establishing shot with a US287 highway sign. US287 is an actual north-south highway running from Montana to Texas through such cities as Denver and Fort Worth. It's possible Sin City is based a bit on Denver's night cityscape, at least its commercial district, but I tend to think the sign is a mislead, the way the Simpsons plays around with the location of Springfield.
(Update @NapoleonWilson: Good note about the La Brea tar pits)
Las Vegas is America's proverbial "sin city" and is located in the west, but there's also the collective "Cities of Plain" from the Book of Genesis, especially Sodom and Gomorrah. Some biblical researchers place Sodom and Gomorrah on either side of the so-called waterfront of the Dead Sea, and one researcher believed they were drowned in the sea -- implying again a city or cities in a basin. Sodom and Gomorrah are also "full of tar pits" according to excavations. The question is, was Frank Miller aware of these particular details when he created the comic, or is it the happy coincidence of drawing on a popular term?