I am planning on traveling to Budapest and Vienna in Early March. I am planning to take the express train (~3hours between the two cities) a Kirendulojegy ticket. I would like to know of a few good places to try to eat local cuisine and enjoy the local culture.
If you want to splurge for an unforgettable meal in Budapest, I recommend the Kacsa Vendeglo (Duck Inn) on the Buda side. The place has been a restaurant for more than 150 years, and walking in is like a time warp into pre-war Budapest. The menu is varied, but the duck is the star, naturally. The mixed Hungarian hors d'oeuvres plate is a great introducttion to Hungarian cuisine's non-peasant side. We both ordered different duck dishes, delivered tableside under huge silver domes. There's a pianist and violinist playing everything from jazz standards to Hungarian folk tunes to classical music. When we saw them, we cringed thinking of the tourist extortion that such "entertainment" usually implies, but they were great, never asked for money (though my husband did ask them if they had any CDs for sale, and they did.) They take credit cards, but they really favor cash (and offered to give us a "free" extra bottle of wine if we paid in cash. Three courses and wine for two--$100.
Vienna means pastries. Demel is the classic spot, and the ice cream creations are every bit as good as the tortes and tarts. The Hotel Sacher is the birthplace for the (in my opinion) overrated SAcher torte--try it and judge for yourself. Viennese coffeehouses are the model for the drink coffee, read the papers, and have intellectual discourse all day lifestyle. Viennese cuisine is, again in my opinion, not worth spending the high prices to see its haute version and too greasy and heavy in its low cost version. Try the Greek (actually Turkish) place that Rick Steves recommends not far from the Opera. Cheap, well executed Greek-Turkish food, carafes of cheap Greek wine, and tasty baklava--all for half the cost of another breaded wienerschinitzel.
In response to Isailtheseas, I am almost positive you are talking about the restaurant "For Sale", across the street from the Nagycsarnok, or the Market, near the bridge Szabadsag, off the corner of Vaci utca. I always find myself going back there, the proportions are huge, the food is great (I'm Hungarian, and their food tastes just as it should).. Too bad the setting was made to reflect the US west, and the name... But the spot never disappoints.