You will not be bored in Budapest, even if you are on a budget. There are several attractions that are free or cheap to visit.
Here are my tips:
1: The transportation passes also cover the public river ferry!
2: Margaret Island: a whole, relaxing day can be spent here, for cheap: ride a bike (you can rent one at the entrance of the island) or try Palatinus water park. Be sure to visit the Japanese garden at the back of the island, and the (free) mini zoo about its middle.
3: Escape the bustling city and hike up to Gellért Hill. Enjoy the sunset from here with some snacks and/or a bottle of Hungarian red wine.
4: Have a glimpse at the Parliament from Batthyány tér. Sit down and enjoy the sunset to see this huge, magnificent building lit up.
5: Walk along Andrássy Avenue to the City Park and have a look at the different architectural styles of Vajdahunyad Castle.
6: Make proper use of our bridges: they are perfect sightseeing routes. Zig zag on them between Pest and Buda.
7: Visit the Castle Hill at sunset and stay until dark: the view of the illuminated city under you is unforgettable. Also, the Castle area is very unique with its lights on and without the huge tourist groups.
8: During the day, take the tour of Matthias Tower since the panorama is amazing from there!
9: St. Stephen’s Basilica: Climb those 354 stairs leading you up to the lookout terrace and enjoy the view of the city.
10: Visit Gül Baba’s tomb and Mansfeld Péter park behind it.
11: Budapest baths are not free, obviously, but you can spend a whole day in Széchenyi Baths, so it worth its price. Take some sandwiches, fruits and drinks with you.
12: Explore the Jewish District and try to find as many street art as possible. Some are huge, some are tiny. There are many design shops and cafés in the district, try some.
13: Do not use the funicular. Climb up instead. Take photos from those cute bridges you see across the route of the funicular. Wave your hands to the people in the funiculars, they wave back, every time.
14: Sunbathe and have a picnic on the stairs of the Hungarian National Museum like students of the neighborhood.
15: Visit the interior of the Hilton Hotel and have a look at how the medieval remains are incorporated in the modern hotel.
16: Eat a lángos at Arany János metro station. Look for Retro Lángos stall – just search for the queue. Try Hungarian dishes.
17: Visit Kossuth square at night to see the Parliament building with its lights on.
Walk along from here to Vigadó Square along the Danube promenade.
18: Explore hidden courtyards and passages. Some of them connect two streets. Unger House is one of these passages.
Once you start peeking into courtyards, you will not be able to stop as you’ll want to go inside every open doorway you come across. Some will hide stores, some will hide coffee shops and some will hide old ladies chatting or sweeping the yard while glaring at you with suspicion.
As Forrest Gump would say: Courtyards are “like a box of chocolates. You never know what you gonna get”.
Recommended areas: Károly körút (Károly Boulevard), Kossuth Lajos street, near Astoria
19. Visit the Great Market Hall and fill your belly with fresh veggies 🍅 🌶 🥒, fruits 
, “lángos” and strudels.
20. Walk along Andrássy Avenue to Heroes’ square. Learn a little bit about Hungarian history while marveling the statues!
21. Learn to use your camera properly while taking photos of the Parliament, Chain Bridge and Fisherman’s Bastion at night!
Tip: for the best night views of the Parliament, walk exactly opposite it on the Buda side. From Batthyány square it is just a few minutes walking.
22. Visit the Shoes on the Danube Promenade memorial that was erected to the memory of the victims shot into the Danube by Arrow Cross militiamen in 1944-45.
23. Take bus no. 21/21 to Normafa and hike up to Elisabeth Lookout Tower. Use the Chairlift to descend from the hill.
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Thanks for this really helpful list. I hope to visit Budapest next year and this will certainly help me find a lot of fun (yet free!) things to do 🙂
This is such a great list! I actually just pitched some articles about Budapest travel tips, I found your share is way more informative! Thank you for share!