We enjoy:
Local culture: Budapest is a very good city to just get comfortable in and do what the locals do. For a lot of that, the location of your hotel will have impact on that. You rule out concerts below,
Food markets: So, the “famous” one is the Central Market Hall from about 1890. It’s a strange mix of tourists and locals. But that ensures that the produce vendors and the meat markets remain profitable (cause Tourists don’t buy pig snouts). But there are a half dozen others around town. I have two favorites one began in the 1890’s and on Saturday morning the inside and a large lot in the back are full of vendors. Every sort of fruit, vegetable and meat imaginable … food booths as well so it’s a great place for lunch. No tourists because it is out of the city center. The other is a modern construction behind a shopping mall. No tourists here either. A mix of produce and meats and cheeses and cafes and … It’s where the locals of our generation hang out. Again, out of the city center. And there is a third come to think of it that is in front of a very nice hotel, in the city center but a few blocks off the tourist trail, so again few tourists. I like the market that takes pace in the park in front on weekends. Yes, for the markets please do try and be here on a Saturday morning.
WW2 history: Well, few places are richer in WWII history, but here its from a different perspective than say London or Normandy. This is about the Holocaust, Nazi collaboration and then Nazi occupation; eventually spilling into Russian occupation. There are tours dedicated to the subject. The past few weeks the Danube River has been low enough for the government to get in and removed a lot of unexploded WWII bombs sitting around the bridges. Generally, once or twice a year a neighborhood gets evacuated while they dig something out of a building basement. There are tours dedicated to the subject. You can visit me too; I own a cold war civil defense bomb shelter. Long story.
Castles: Well, you got me on that one. There is Buda Castle but it’s not a classic castle. It does have foundations back to 13th century I believe. And I believe there are some basement tours that get you close to that. As an interesting place to visit … hard to beat. But castle? Debatable. Then there is the castle in the city park. Built in 1896 for the 1000 year anniversary of Hungarian nationhood. It combines details from a number of castles in Transylvania (use to be Hungarian). Castles are just not the thing here.
Walking tours: “Free” or with paid guides or from Rick Steves do it yourself list or I have a couple that I like. They are in what I sent you. Walking the streets here is very enjoyable and when you get tired with have a great set of trams to get your around with a view. Free if you are 65 or older.
Architecture: It is so good that Anthony Bourdain called it Architectural pornography. There is no old town, but the old part of the city is nearly 10x larger than the tourist district in Vienna or Prague. We have some big names like the parliament and the opera house, the Buda Castle and Mathias Church and the Basilica. But there are some hidden places of interest like a wonderful old library. And to be honest every bit of the old part of town is fascinating.
Churches: We do have a couple. The Basilica in Pest and Mathias in Buda. Most tourists miss the inner-city parish church which sits on Roman ruins and dates to the 11th century. But there are more spectacular churches in the world. We also have synagogues. The largest in Europe is here and it’s stunning. Within about a 10-minute walk are 2 other fascinating and beautiful synagogues and another handful around town that the tourists always miss.
Nature: For that we have Margrit Island and City Park and they both do a pretty good job at reflecting it.