Sarajevo has a very small city center. In 1-2 days you can see the entire city. Most of the toruistic things can be seen in one main Road and along the river Miljacka.
Things you can see in Sarajevo:
-The Latin bridge where World War I started whith an adjiacent musuem where you can see the reconsturcton of the attempt to Ferdinand of Austria.
- The Old Towm or Ottoman District where you can see one of the most beautiful Mosque of Europe. While you are in old town you can buy a carpet, smoke shisha with different fregancies, eat Cevapi with Yougurt or Burak or traditional Bosnian sweets made with honey. Alchool is forbiden in this area but you can find lots of good beer around this place.
- The Libary in Ottoman style that is currently under reconstruction
-The main road of the city for shopping. But here you can also see the Catholic Church of the city, the main theather, and nice Orthodox Chruch with some moe mosaic. On the main road there is also a huge skycaraper where you can see all the entire city.
-Then I suggest to have a look at the olympic village
- and along the river see the Jewish Sinagogue, the Art Accademy that looks like the architecture of Budapest, The Eiffel Bridge, The Bosnian parliament
-Last thing Bosnian National Museum where you can see Bosnian archeology from Pre-History to Modern Times.
Then there are other few things..but that the main part..
Then I suggest to go to Mostar, another city where you can see the Bridge and the Amazing nature of Herzegovina ( Mountians, Lakes, Rivers) If you like hiking thats the place!