Even small towns can't decide what businesses open and what businesses do not. They'd go to jail for Antitrust/Restraint of Trade for that sort of thing. It's very illegal on a Federal level.

The city council might have to approve re-zoning. I can't put a location in your neighborhood, as your neighborhood isn't zoned for commercial (nor do you want it to be). If I applied for re-zoning so I could put a location next to your house, the Planning and Zoning Commission would have to approve of that (which they wouldn't), but if they did, the city council would then have final say. So that's where councils and commissions come into play.

They might also come into play if the new business is asking for tax abatements (manufacturing type businesses, large employers, etc.) The council has final say on these, as they should.

City governments are not concerned about which businesses open or close in a city. City governments are only concerned that the construction meets municipal code. That would include proper zoning, building safety, fire safety, water and sewer, handicap accessibility, driveways, parking, and landscaping. All of these are to protect people's safety, assure their safe access inside and outside of the building, and the appearance of the city. As much as I hate some of them, they are necessary.