A popular chain of hummus restaurants around Budapest. Friendly staff and good food for affordable prices. All restaurants more or less share the same menu but some are vegetarian-only. My recommendation: Shakshuka (with mergez sausage if that's your thing)
Mexican restaurant. 2-course daily menu Editor's recommendation: the Club Sandwich
Best burgers in Budapest.
Seafood restaurant with high quality products. Pricy. My recommendation: Fish & Chips
Hungarian-style restaurant located in the district of Óbuda. Not centrally located but easily reachable by public transport (tram 1 or HÉV). Open 24/7. Tasty food and huge portions.
A small restaurant on the banks of the Danube. Ideal for a quick toasted sandwich or a nice brunch.
Located next to the market on Hold utca. Very good meat selection. Friendly "mom-and-pop" atmosphere but very small.
Greek restaurant on the river banks. Friendly staff and good food.
A chain of all-you-can-eat (and drink) restaurants in Budapest. Their prices vary by location and by day.
Raw-food restaurant in Budapest (probably the only one). Located near the Parlament.
Vegetarian restaurant with tasty indian dishes. Very cheap.
Old café where Hungarian intellectuals used to meet. Small menu but good food. Located in Buda, not too far from the Gellért baths.
The restaurant is almost litteraly a "hole in the wall" but don't let it fool you. Its Belgian-style French-fries are one of the best in Budapest. Sadly, the rest of its offerings (like the burgers) isn't quite as good.
This bar in the jewish district also has a very good menu. My recommendation: Go with a friend (or three) and try the Serbian meat platter (huge portion).
This Scottish pub also serves delicious hamburgers and traditional Scottish food like Haggis. You can even find some Irn Bru: Scotland's signature bright orange soft drink. Very friendly atmosphere, especially if you go in when there's a rugby game on TV.
A good restaurant with cheap daily offerings close to the center. Note that they only accept cash. My recommendation: Rakot Krumpli with sour cream and sour cucumbers. A classic Hungarian dish made of layers of baked potatoes, spicy paprika sausage and eggs.
Italian restaurant near the center. The payment system is unusual but works quite well. You get a magnetic card when you enter and use it when ordering. When you leave, your card is scanned and you pay for what you've ordered.
There are three counters: Salads, Pastas and Pizzas. At the salad counter, you can make your own composition out of fresh ingredients. For pastas, you pick a sauce/dressing out of the menu and you can choose which type of pasta you want with it. Your dish is then assembled in front of you (the chef makes the sauce while the fresh pastas cook within a few minutes) Pizzas are freshly baked on order.
Note that it can get quite crowded around lunch time but the lines move fast (tip: there's usually less people queuing for pizzas).
A small place where there's barely ever anyone but the food is great.
My recommendation: the Pastrami sandwich.
Very good and affordable New-Orleans style "soul food".
My recommendation: try the ribs or the chicken wings.
A newly-opened chain of bakeries from Croatia. My recommendation: Meat (or fresh cheese) burek with a yogurt drink. A tasty specialty from the Balkans.
Cserpes is a famous dairy producers that supply many shops and restaurants in Budapest. This tejívó place also serves delicious and cheap sandwiches. My recommendation: Mangalica sausage sandwich and a "Cocoa Snail" (kakaós csiga) for dessert.
The best pogácsa in Budapest and delicious cakes too. Far from the center but the trip is worth it. The place might seem inconspicuous but the long lines at its entrance don't lie. My recommandation: A bag of cheese pogácsa for a salty treat or a slice of Esterházi torta.
Best kakaós csiga in Budapest.
Old-school confectionary where you can try the Hungarian specialty called rétes. Similar to the german strudle, there are many different fillings: apple, sour cherry, fresh cheese or poppy seeds. For a different taste, try the cabbage one.
You like reading? You like donuts? Welcome to the Donut Library where you can enjoy your favorite sugar-bomb treat while reading a book from the shelves (in Hungarian only). My recommendation: the pistacchio donut.
A large selection of sweet and savory bakery products. Ideal for a quick bite. My recommendation: the cheese pretzel ("sajtós perec")
Home baked cookies in a relaxing atmosphere. Large selection of home baked products and friendly staff.
Both a candy shop and a novelty bakery. Not the best bakery in Budapest but definitely the most unique-looking. If you're a fan of Jelly Beans, you can buy them by the color.
Best icecream chain around Budapest. My recommendation: Real pistacchio icecream.
Artisan chocolate maker in the center of Budapest. Despite its central location, it's a bit hard to find since it sits at the end of a narrow alley. My recommendation: The Trabant-shaped chocolates (the famous communist-era car that was popular in Hungary some decades ago).
Budapest's biggest market hall located on the banks of the Danube, at the foot of the Liberty Bridge (Szabadság Híd). Impressive architecture and a good way to taste local products. It's closed on Sundays and only opens till 3pm on Saturdays (wekkday opening hours are 6am - 5pm). My recommendation: Make sure you visit the top floor and try a fried sausage (sült kolbász), served with a thick loaf of white bread and a copious amount of mild mustard.
I think this list is great. I would add on thing only to it: a strew burger place named Zing Burger, which is at the Gozsdu Udvar, the latter is full of great places anyway. I myself am a big food lover, so I can put things to the list if needed.