Budget
Sarajevo has countless shops selling burek meat pie, sold in layers by weight or by piece, Äevapi and pizza stores. Pita burek, sirnica, krompirusa, tikvenica, zeljanica etc is a filo type pasty pie generally offered in several varieties - meat meso, cheese Bosnian cheese called "young cheese" similar to ricotta and never aged sirnica, cheese and spinach zeljanica, pumpkin tikvinica, and spicy potato krompirusa. It is usually served with a traditional yogurt sauce which resembles sour cream. Most Cevapi places do not serve alcohol.
Midrange
Bosanska Kuca
Seats inside and out in the heart of the old town with a wide range of traditional Bosnian food at reasonable prices. You can sit outside against the warm wall of the oven if it's chilly.
Hacienda
Mexican food, cocktails. Large portions with very fresh ingredients and a pleasant atmosphere. DJs are playing House and Techno Music. Comparing to some other similar places, Hacienda is more expensive but still with good atmosphere.
Karuzo
While it doesn't serve traditional Bosnian food, this restaurant features a vegetarian/fish based menu, with a mostly Italian influence although sushi is also available. The pasta dishes are also highly recommended. It's a very intimate restaurant seating only 18 at a time, the chef takes your order prepares the food and serves it himself. Do be aware that you probably do need to have a good deal of time to spare - it can take a couple of hours before you leave.
Bambus
An amazing jewel of a restaurant in the central shopping district. You have to go down a small staircase and push a button to be buzzed in to the restaurant but once you are there you will be happy you took the time to find it. It is very classy, quiet, clean, English menu and the waiters speak English. Very good food at good prices. The food is cooked with pride and for the prices charged, it really is a good deal.
Ottoman Kebap House
Turkish restaurant on a side street in the old town. The inner courtyard lets you eat outside while being away from the noise of the street. The staff are friendly, and will cook the food to your desired level of spiciness.