Szeged is famous for its local, traditional food.
The most famous of all is probably the Fisherman's soup Halászlé, which is made from various freshwater fish using lots of paprika this is not necessarily spicy, but you can definitely order it that way.
Szeged is also known for its good quality sausage and salami. Pick is Szeged's own brand, which is also exported to various countries around the world. Make sure that you try the famous "Pick salami". You can buy these products at most local grocery stores and smaller, family owned 24/7 stores.
If you are looking for international food, just check the local grocery stores. You shouldn't have too much problem finding anything from around the world. Even Americans can find their favorite cream cheese and peanut butter/jelly if they look around...
restaurants
The quality of the food varies by restaurants, but is good in general. Meats and cheese can be found at most places, and they are often breaded and fried. If you go to a standard restaurant, the portions will be generous and more than enough to feed an adult. There are a few restaurants GÅry (http://www.gory.hu/), which serve extra large portions of food, which are almost impossible to eat all at once.
In the downtown Tisza Lajos krt. 76. there is also a vegetarian restaurant (http://www.agnietterem.hu/) serving traditional Indian and Hungarian dishes as well.