LIKE much of post-Communist Europe, Budapest has replaced the image of the impoverished East with symbols of international luxury, like the Four Seasons Hotel Gresham Palace and a new branch of Nobu, the high-end Japanese restaurant. But unlike many other cities in the region, the Hungarian capital’s brightest spots are often native-born, rather than imports. From stately Buda in the west to Pest’s shabby-chic streets east of the Danube, a range of new attractions show off the achievements of local artists, producers, vintners and chefs. Even if you don’t end up tasting every last domestic food specialty identified as a “hungarikum,” or tracking down every up-and-coming designer, a weekend here provides a glimpse of the city’s justifiable pride, as well as an authentic sense of place.