Eating and drinking
Streetfood
hummusbar - hummus bar
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The name tells it all. It is a franchise with lots of locations in Budapest. Each of them have some small differences. This one in the Október 6 street has laffa baked in a traditional oven.
Trattoria Pomo D'Oro
https://maps.app.goo.gl/qxh4onVmRZG387mr8
A bit upscale pizza restaurant in downtown Budapest. I've never been here, I like Pizzica more and it is only 15 min walking distance form Pomo D'Oro.
Sao - asian
https://www.facebook.com/saofoodandbar/
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This is maybe the best pizza place in the Buda side. It is more upscale than Pizzica and have more sitting places, but it has less authentic vibe. The name igen, means yes.
Upscale restaurants
MAK
https://maps.app.goo.gl/kmFY7EPmcua9u3FV7
Fine dining restaurant with tasting menu. The usual fine dining things, using local materials from Hungary or neighbouring countries, all organic and so on. I've been here only once a loong time ago.
Costes downtown
https://costesdowntown.hu/etelek-es-italok/
https://maps.app.goo.gl/M4qdaQxWETs69y5n8
Fine dining restaurant with tasting menu. Its brother restaurant was the first restaurant in Budapest to receive a Michelin star. I've never been here, it is just too expensive 
The owner of the restaurant is the same person who started and co-owned the Sziget festival.
Bakeries
If you like pastries you need to try "Kakaős csiga" cocoa spirale and "Túrós batyu" cottage cheese filled thing.
Butter Brothers Bakery & Bistro
https://www.butter-brothers.com/
https://maps.app.goo.gl/nXtFUAaVHS74bkm79
Best kakaós csiga in Budapest.
Bars
Kisüzem
https://www.facebook.com/Kisuzem
https://maps.app.goo.gl/ZtmPqTYXcQMAxh5r6
A typical bar in the middle of the former ghetto with underground and hipster crowd. It has some good food also and sometimes it operates as a galery.
Toldi
https://maps.app.goo.gl/p4UZhXvrnZWmXXuJ6
Bar and party place in the lobby of a cinema,
Szimpla
https://maps.app.goo.gl/WeGT9Pu52GUH2N266
The mother of all ruin bars in Budapest. During the early 2000's a set of new places opened in the unused building of the inner city and they lighted the vibrant nightlife of the district. This was the first bar like that and it is still a classic. There are lots of tourists here as this place is also advertised heavily in tourist magazines.