Budapest's Central Market Hall is a must if you're at all interested in learning more about Hungarian cuisine. The market itself is massive, probably the biggest one I've ever seen in my life, and it's spread out across three floors: the basement area full of preserves and pickles, the ground floor mainly serving meats and vegetables, and the top floor for souvenirs, textiles, and restaurants.
The market walks a fine line between local favorite and tourist trap...there were lots of locals there doing their weekly shopping, but there were also a lot of stands obviously designed to sell kitschy and overpriced items to tourists, so you really need to explore the space to find the authentic stands. It was really interesting to check out the various cured meats and sausages on offer, as well as the endless amounts of cheeses I'd never seen before. Most of the vendors speak English so don't hesitate to pick up a few slices of what looks interesting and dig in!