The Great Market hall, located at the noth end of Vaci Utca, offers fresh produce and meats, as well as traditional Hungarian foods and souveneirs.
The beautiful outer facade of the the market hall is the subject of many photos, and the spacious interior with all of it's stalls and shops creates a bit of a workout for senses. The smells of paprika, meats, produce and the somewhat chaotic sounds and atmosphere makes this a memorable stop in Budapest. If you're looking to buy cheap food this is the place to go. A kilo of tomatos for example will cost around 150 HUF. Also available are various varieties of Hungarian sausages and salamis too numerous to list here.
On the second floor of the market is where you'll find the touristy souveniers such as tableclothes and t-shirts, however you'll also find some small eateries where you can fill up for a decent price. You can also buy some cheap wine in 2-litre bottles from locals for around 400HUF.
A favourite of mine are the stuffed paprika peppers available in the basement of the market. In the basement of the market you'll also find a small "Smatch" grocery store and a number of smaller shops carrying seafood and different paprika and peppers.
While the market is admittedly a bit of a tourist trap, especially the second floor, it's still where many locals come to do their shopping and it still retains a strong authentic Hungarian character, and is certainly worth a visit.