Here’s a few recs of personal favorites:
Wirtshaus “Henne” (Xberg) – fried chicken.
The Bird – (Pberg & Mitte) fab burgers. Their newish place in Mitte also serves really great bbq (think brisket, beef ribs, etc.)
Friedel Richter (Mitte) – menu changes daily. Fried chicken skin app.
Cocolo Ramen (Mitte)
I Due Forni or Standard Pizza (Mitte) – great pizza
Terra Sarda – fab and very budget-friendly Sardinian place
Katz Orange (Mitte)
Txokoa (Neukölln) – Basque food. 24-hour braised pork belly. really good
Yarok (Mitte) – great Syrian food
Les Valseuses (Pberg) – French bistro
Karloff (Xberg) – tiny Italian place w/a daily changing 4-course menu
Not sure if you are interested in cocktail bars, but Reingold (Mitte), Beckett’s Kopf (Pberg), Stagger Lee (Schöneberg) and Lebensstern (Schöneberg) are all great in their own way.
Also, not sure when you will be in Berlin, but the Thaiwiese @Preussenpark is not to be missed when the weather is nice enough to be outside. The local Thai community sets up numerous stands in a park, and the food is fabulous and cheap. Killer som tam, excellent soup, curries, noodle dishes, and boozy drinks galore. You can also get a massage while you’re there
Another favorite of mine is the Saturday market on Winterfeldtplatz (Schöneberg) – not just for grocery shopping, but for lunch. Steckerlfisch offers whole grilled fish or fish filets, there’s a Swabian stand, and another favorite of mine, a Thai cart that sells amazing “dim sum” – the spicy ones in particular are addictive.
Lemme know if you’d like any more advice on specific cuisines (also, I’m sure I forgot a bunch).
As for Hamburg, get thee to Nil. Really wonderful place with modern German food and super-friendly service.