If you want to get away from foreigners, forget about Szimpla Kert and Gozsdu Udvar, as they are mostly packed with tourists. You have a higher chance of sharing a drink with a Budapestian at one of the city's (in)famous dive bars. But if you and and your friends are up for something fancier, we would recommend some spots on Kazinczy Street. Yes, while this area is popular with tourists there are also spots where the local young things of BP go to party. Check out Tesla or Mika Tivadar Mulató for example. As a more low-key alternative to one of the party spots at Gozsdu, we recommend Telep or Központat the nearby Madách Square. Akvárium or Barba Negra Music Club can also be a good destinations - not just because they are popular live music clubs, but because mostly Hungarian bands play there so you can get a sense of the local music scene.
If you are a fan of hiking, but tired of the tourists, skip Gellért Hill and visit Normafa. The view is breathtaking of Budapest from there too, and you can have a picnic or eat a rétes (Hungarian fruit strudel) at one of the stands. Margaret Island is popular amongst Hungarians and tourists, but if you want to experience the capital like a local, we would advise you to explore other green areas in the city. At Füvészkert, the country's first botanical garden, you can find 150-year-old maidenhair trees, orchids and hundreds of cactus varieties. If you are longing for a riverside setting, Kopaszi Dam is a hidden oasis in Budapest. Acres of landscaped greenery and modern restaurants, that are open in the warmer months, await you on the Buda side of Lágymányosi Bridge. Another option is, instead of taking a touristy boat tour of the city, jump on the BKK boat (which operates in the warmer months) and head to Római Part(Roman Riverbank in English) where you can relax on the riverbank and eat some fried fish.
Budapest is famous for its thermal baths, that's a fact. But many visitors don't know, that although Gellért Bath is the most well-known of them, most of the locals prefer Rudas. Rudas is cheaper and it still has everything - saunas, steam rooms, sunbathing terrace, Turkish baths and jacuzzis.
The tourist magnet that is the Museum Of Fine Arts has closed its doors while it undergoes renovations, giving art-lovers a great opportunity to immerse yourself in the independent art gallery scene of Budapest. You could visit contemporary art galleries like Chimera Project, Trafó Gallery and Higgs Field. If these are a bit too underground for you, we can recommend the Ludwig Museum.
Uránia National Film Theatre is one of the most famous cinemas in the world, and popular amongst locals too. But you might want to skip it and focus on the hidden gems like the smallest cinema in Europe: Cirko-Gejzír, where they usually screen independent and/or art-house films. Örökmozgó is also popular amongst locals as they often screen cult classic movies and rarities from the collection of the Hungarian National Film Archives.
Hungarian people prefer wallet-friendly eateries over Michelin Star-priced restaurants. One of the most "local" things to do is to is to eat the "napi menu," which is the budget lunch offered by most of the places in downtown Budapest. This is usually two or three courses for about 1000 forints. Of course tourists might also like to experience the best of Budapest's fine dining, so hit two birds with one stone by trying one of these luxurious lunch menus. If luxury isn't your thing, then pretty much all of the restaurants you head to will have this lunch menu option - be sure to arrive at about noon as most of these places only cook up a limited number of the cheaper lunch menus, and you'll be competing with all the locals to get them!
