Growing up it has to be Zero Boys. They were long broken up by the time I was old enough to learn of them but for Indianapolis they'd be THAT band. Located in the Bay Area now and I don't think there's a single band who fits the bill. Depends on who you ask and what scene they were from. Interested in how people from smaller scenes answer this.
HOMETOWN BANDS
Coldwater, Michigan is where Jad and David Fair are from, but they started Half Japanese after moving to Maryland. Their brother Pete used to be my neighbor.
Kalamazoo, Michigan it's the Spits.
Crockett, CA can claim Naked Lady Wrestlers. Could be worse.
Santa Fe only has Beirut, which fucking sucks. Millennial REI wife music. On the upside, Gregg Turner from Angry Samoans lives out here.
I'd start a band but ppl only like craft beer bluegrass in this town.
The heroes of South Florida! I was too young to see the Eat on the first go around but got to see them several times in the mid 90's and again in the early 2000's. They were still great and the Hialeah 7" is every bit as good as the first two 7's. I grew up just down the street from Eddie O'Brien. I bought two copies of God Punishes off his 12 year old son. He thought his dad and uncle were lame and wanted weed money so I got them for $20 a pop! My teenage girlfriend also crashed her car into a tree in his front yard. Poor guy! Mike O'Brien was always around and at shows well into the 90s and had an awesome band called Drug Czars. It was quite a thrill to have Mike show up to a post show party I threw at my parents house while they were out of town.
South Florida was a great place to grow up. All the old punkers were still around and hanging on the scene. I used to get invited to the cool older punk parties (mostly because I always had coke), and would listen to them tell stories about the old days and wild tales of Teddy and the Frat Girls. My first rock n roll crush was Lisa Hodapp (Morbid Opera) and I'd follow her around like a puppy dog. I thought I was playing it cool, but years later when I introduced her to my new girlfriend (who had a Teddy and the Frat Girls cover band) she said "You know Rich used to have a crush on me, but I guess he won't have to follow me around anymore." haha.
Here's The Eat playing on local television. Their drummer, Chris Cottie, was the touring drummer for David Allen Coe before joining The Eat. RIP Chris Cottie, and Mike O'Brien.
Rocket from the Crypt had a hold on San Diego.
Skip Spence was a known drifter in both Santa Cruz and San Jose
B.F. McGee-zax Unfortunately, the “punk” band that SD is most known for is Blink 182. 
We also had Battalion of Saints, The Zeros, The Injections earlier on but then the pop punk, ska, emo/screamo scene gobbled all the real shit up.
Vinnie Vacuum Skip Spence aside, what would be "the" SC? Camper Van Beethoven (not my choice but seems it'd be a popular one)? B'Last?
60's jangle/folk rock from SC, later morphed into Harpers Bizarre. Idk if they'd be THE SC band but I always liked this track. A rare interesting artifact outta my town. And yes B'Last might be the best "punk" example, but not a band I spent a lot of time with so idk I guess I'm kinda shooting blanks here.
Vinnie Vacuum That's a nice little tune. Never heard them before. I spent a year and half living on Pleasure Point and about the same amount of time in Scotts Valley. 1990s.
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Lived in Newark, CA for a couple of years. Can't think of anybody from there except the Cliftons. Very Dwarves-y. Featuring Jonny Manak, skater and member of Jonny Manak and the Depressives.
Thank you all for sharing. <3
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I would say Camera Silens is THE hometown punk band everyone knows and loves here in Bordeaux, France.
Love this prompt! Born & raised Portlander here, I'll corroborate The Dead Moon answer. Fred and Toody are beloved bastions of the punk community and have contributed so much-not only through their own music, but through institutions like Captain Whizeagle's, and supporting local music scenes/makers in countless other ways.
The Rats are also way up there for me. On some days I even like them better.
Also The Wipers, a group with a sound both distinctive and emblematic of a dark, slightly off kilter and almost dreamlike quality that I associate with a lot of Portland bands.
My Dad was a fixture of the Portland punk scene in the 80's and the name Poison Idea was uttered with utmost reverence in our house. Also Dean was a regular at this restaurant i used to work at. He was very cool and nice and I wish i would have pestered him for more stories. The influence of "Pick Your King" etc. Can't really be overstated.
Lastly, Neo Boys. Not because they are particularly flashy or face-ripping, but they have a raw melodic potency that touches my heart.
I’m from Dartford. My hometown band is The Rolling Stones.
San Jose garage:
Count Five
Syndicate of Sound
Chocolate Watchband
I guess for Columbus the most obvious one is The New Bomb Turks, and that was definitely the case for me through high school. Was so incredibly excited to see them for the first time (same day as the Gibson Bros. reunion; had to miss the Oblivians at the after party because I was 17 haha). I guess at this point, the Cheater Slicks could also count, even if they are transplants.
But we also have a lot of figures who embody what the city's underground music is all about: Ron House, Mike Rep, Don Howland, Tommy Jay (R.I.P.), and Jim Shepard (R.I.P). There's a ton of great music spread across their discographies. So for me, I guess the real hometown band is the one-off Ego Summit project, which could be the best record ever out of this city.