I need to preface this by saying: this is not the same as where to eat in Berlin if you're a local. Living in Berlin I go out to eat a lot, but my go-to cuisines are Vietnamese, Greek, Italian, and Middle Eastern. Also, I mostly go out to eat in my (lovely) neighborhood, but unless you are a gay man, there aren't exactly many tourist attractions nearby. Also: in my view, the German dining experience is first and foremost about the experience - ambiance, decor, and coziness are highly valued. The food is secondary. Which is to say, the food is usually good but often standard, I don't see much striving for creative and amazing in the culinary department. But that's just the food snob in me talking. ;) My advice is to go with it - seek out the restaurants in a great setting with a cool scene, and just soak it in. There are definitely some vibes to be found that I have never experienced in the U.S.
Typical Berlin food
Classic Berliner "cuisine" consists of currywurst and döner. Which is basically drunk food. But also legitimately delicious! You can find it everywhere, but there are some clear bests in this category.
Currywurst is essentially a hot dog with (mild) curry ketchup. It might not blow your mind, but I find it to be pretty tasty fast food. The classic is Curry 36, with locations at Mehringdamm and Bahnhof Zoo (aka Zoologischer Garten). If you want to pay twice as much but feel good about eating organic, I can recommend Witty's at Wittenbergplatz (by Kaufhaus des Westens/KaDeWe).
The best döner can be found at Mustafas, which happens to be across the street from Curry 36 at Mehringdamm. There is quite often a line, but if you arrive at a weird time or when it's raining, then you might luck out and not have to wait. If you do have to wait, do like the locals and get your beverage of choice (which probably should be a beer or maybe a Club Mate) to consume while you're standing in line.The meat at Mustafas is chicken, elsewhere it's more typical to find lamb. I've been meaning to try out a couple of other döner places by Kottbusser Tor - check out this list if you're interested. Warning for the faint of heart: Kotti, as it is affectionately known, is kind of dirty and trashy. Berliner hip kids love it anyway (or maybe because it is so trashy). Things get prettier a few blocks away, but this is not where I'd bring my family on a trip to Berlin.
Other German favorites
Maultaschen are the German version of ravioli, and I love them - especially because the standard version is filled with meat, not cheese, which means I can eat it! If you are hanging around Unter den Linden/Brandenburger Tor (which you probably will be at some point), I can heartily recommend Die Maultasche for a quick lunch. It is unassuming, untouristy, and authentic. Authentic southern German that is-- Schwabian to be precise -- this isn't Berliner cuisine. For a hearty dinner I can recommend Maultaschen Manufaktur, not too far from Potsdamer Platz and right next to my favorite dive bar Kumpelnest 3000.
Beer and pretzels...sorry guys, you should really go to Munich for this. There is plenty of good beer to be found in Berlin, but it isn’t the traditional German beer you probably expect. (Bottled, you can of course get traditional southern German beer – my favorites are Augustiner and Rothaus.) I cannot drink the bigger Berlin beer brands, which include Berliner Pilsner, Berliner Kindl, and Schultheiss. I know I am a snob, but ick. The good news is, the craft beer scene is getting big in Berlin, but they are mostly producing west-coast style IPAs. So if you are visiting from the west coast of the USA...maybe this isn’t so exciting. Or if you are a beer connoisseur, maybe you can pick out the finer differences between Berlin hipster beer and west coast hipster beer, I don’t know. I really like Heidenpeters, which can be found in Kreuzberg in Markthalle IX, and sometimes elsewhere if you’re lucky. I’ve always wanted to go check out Eschenbräu, which I expect is less hipster. Or check out this guy's list of the best craft beer bars in Berlin.
As for pretzels, they are simply better (and bigger) in southern Germany. If Munich is on your itinerary, get a pretzel and a Maß (1L beer) at the Chinesischer Turm in the English Garden, and the pretzel will be delicious and as big as your head.
Other German restaurants to try in Berlin:
Joseph Roth Diele. Not far from Potsdamer Platz, this place is supposed to be good. But it's not open on Saturdays or Sundays!
Zur Letzten Instanz. Near Alexanderplatz, this place claims to be the oldest restaurant in Berlin. I've never been, but it's on my list of places to try out when visitors are in town.
Mutter Hoppe. My (completely awesome) German hairdresser tells me this place is authentic "Berliner" food and great for guests. Also near Alexanderplatz, it's also on my list. Reservations recommended.
If the weather is good, you should do like the Germans and consider only restaurants with outdoor tables available. Almost every restaurant that wants to have customers in the summer will have some sidewalk tables. That being said, there are some places where it’s extra nice to sit outside.
The concept is simple, and awesome. Sit outside at picnic-bench type tables, and eat and drink. Beer Gardens in Berlin don't have the same traditional feeling as those in southern Germany, but they have their own flair. Food and drink are self serve. These are my favorites in Berlin.
Cafe am Neuen See. In the middle of Tiergarten, a very leafy atmosphere complete with small lake and row boats. It’s lovely, and rather fancy as beer gardens go. Rather untypically, the go-to food here is pizza. Cafe am Neuen See also has an indoor cafe that’s quite cozy in winter, complete with roaring fireplace.
Schleusenkrug. Also in Tiergarten, an easy walk from Bahnhof Zoo (Zoologischer Garten). On the canal, also very green, and a good place to watch soccer in case the German national team is playing. Wide selection of food that’s good for vegetarians, though prices are high by Berlin standards (which means normal by anyone else’s standards). This is my go-to beer garden, in part because it’s close to my house. ;)
Prater Garten. Berlin’s oldest beer garden, located in Prenzlauer Berg. Ever so slightly punk rock, especially compared to the rest of Prenzlauer Berg. I don’t get here too often because it’s way across town for me, but I like it.
Cafe behind Haus der Kulturen der Welt (House of World Cultures). Right on the Spree river, not far from the Reichstag, this is a nice sunny place for a beer or a snack. As a bonus, you can pick up tourist boats here which will take you into Mitte.
Cafe im Literaturhaus. A bit off Kudamm, this is a quiet little oasis that’s great for a light lunch or coffee and cake. They also have an indoor “winter garden,” which is a little less casual.
Cafe Einstein Stammhaus garden (in the back). This is in the style of a Viennese coffee house – the interior is quite nice AND a scene from Inglorious Basterds was shot here. My favorite place to sit, though, is in the back garden. The best thing on the menu is the Apfelstrudel, though they also do a beautiful-looking brunch. It’s slightly pricey (again, by Berlin standards).
Prinzessinnen Garten. The real reason to come here is if you're a fan of urban gardening...this is a super cool and creative community gardening project. They also have a leafy outdoor cafe, perfect for a beer or a fruit juice schorle and cake. They serve one warm lunch dish each day and pizzas in the evening, and everything is vegetarian, with veggies from their own garden. A true oasis in the middle of Kreuzberg. Note that they are not open in winter (the season runs roughly from May-Sept.)