Hamburg in September

https://www.reeperbahnfestival.com/en

In Hamburg besides Superbude sleeping on ships is authentic and an experience - also few other approaches.
https://www.hamburg.de/aussergewoehnliche-hotels-hamburg/

A roastery visit is somehow must-have.

Local food specialty is Labskaus and desert Rote Grütze.
Cheap and good fish you wil get at Fisch & So.

Bus line 111 takes you around some sights.

thank you!

I stayed near the Sternschanze area a few years ago and enjoyed the neighborhood. It's pretty lively, especially in the evenings. I stayed nearby at a unique hotel, built inside an old water tower, photos.

MarkK already covered most of it. Krabbenbrötchen, Aalsuppe (no, it isn't eel despite what the name might imply), and Franzbrötchen for dessert are other local dishes. A place to eat local cuisine is the Oberhafen Kantine. Or pop into the restaurant at the Krameramtstuben.

Sternschanze, as you said, is a trendy area; you'll want to check out the Rote Flora. You might also like the Bunker St. Pauli ( https://www.bunker-stpauli.de/ ) and all the areas in between--Frank&Frei, Omas Apotheke for brunch, Altes Mädchen / Ratsherrn Brewery tour (okay, the tour isn't super amazing, but it's a great place to have a beer). Also on the trendy end for younger people is St. Georg.

Have a beer at the Überquell and check out Park Fiction just behind it. Also, the Fischmarkt on Sunday mornings is a MUST--go early (5am) or stay out all night and end your party there. Visit the StrandPauli for a cocktail if the weather is nice. Along that walk is a little bar called the Haifischbar. That could be worth popping in for a beer or even just to take a quick peek.

The Reeperbahn tour is very much a must if you don't have kids with you, and at the end of the Reeperbahn there are the Dancing Towers. At the base is a brewpub called Brew Dog, and the language there is English. Great beer selection. Across the street is the rock pub Zwickl, which some people might enjoy seeing.

Need your "old town" fix? Much of Hamburg was bombed, but two streets worth seeing as you walk around town (and they really are right there in between everything and can be walked through from A to B) are the Peterstraße and the more well-known Deichstraße. For the latter, be sure to pop through the little alleyways onto the pontoon to see them from the water.

If the weather is nice, you can also rent a kayak or SUP or the like and see the upscale neighborhoods by paddling through the canals of the Alster--very relaxing and pretty. Spanische Treppe is a great starting point for that.

Locals also enjoy nice weather at the Boberger Dünen (sand dunes right in the city), Falkensteiner Ufer / Blankenese beaches (you can see shipwrecks at the latter at low tide, and the walk through the Treppenviertel down the hill to the beach is nice), and the various parks, with the Stadtpark and Altonaer Park being the most popular.

Of the don't-miss tourist sites, Miniatur Wunderland (for most people), the Elphi, walking along Landungsbrücken, and St. Nikolai are definitely "don't miss." You might enjoy popping down into the Old Elbtunnel.

In September, you may want to head down to Jork and check out the beautiful village and apple orchards. Or visit the Kiekeberg outdoor museum and see what old farmhouses in northern Germany were all about (you can hike a bit there as well).

Okay, that's a few of the off-the-tourist-track and a few on-the-tourist-track recommendations.