One of the best things about Sarajevo is all of the things you can do around Sarajevo. If you have the time you should certainly try to make a trip or two (though not at the expense of truly seeing Sarajevo).
Bosnia and Herzegovina is filled with wonderful things. In close proximity to Sarajevo you can swim in a mountain top lake, visit a Cold War era nuclear bunker that was secret for decades, and go skiing at a ski resort that hosted a winter olympics.
You can even visit what is allegedly the world's largest pyramid (I have my doubts), visit one of Europe's most remote yet inhabited villages, and so much more. Of course, Sarajevo is not the only town in the country and you can visit others too, like Mostar and Trebinje.
Not many people actually know this: you can ski in Bosnia and Herzegovina on what are commonly referred to as its 'Olympic mountains'.
More than this, Sarajevo hosted the 1984 Winter Olympics. The competition was hosted at numerous locations, with the two primary locations less than one hour from Sarajevo.
Day passes and ski rental are cheap and if you have time it is well worth spending a day or two on these slopes.
While it may not have as many lakes as say Sweden, Bosnia is a country with a lot of lakes. You can swim in mountain lakes and lakes with islands and monasteries in the middle.
If you don't like lakes, or you find swimming a bit pedestrian, there are also rivers you can go rafting on (in?), thanks to the country's ruggid landscape.
Unbeknownst to many, Bosnia also has a (very short) coastline and seaside resort at the town of Neum (sandwiched inbetween Croatia on either side).
There are a lot of hills and mountains in Bosnia and Herzegovina. The closest to Sarajevo is Mount Trebevic, which overlooks the city and is connected by a convenient cable car.
Bosnia is also traversed by the Dinaric Alps, a mountain range stretching from Italy to Albania and considered to be among the most ruggid and extensive mountain areas in Europe.
The highest peak in Bosnia and Herzegovina is Maglić, at 2,396m, but you'll find excursions for all levels, and may even come across some wild horses and some of Europe's olderst forest on the way.
Bosnia and Herzegovina is home to many indicators of extensive human inhabitation. There is a cave drawing dating back to 12,000 BC, there is evidence of Illyrian tribes, Roman conquest, Avars and Slavs, as well as Autro-Hungarian and Ottoman occupation.
Locations across the country offer interesting insight into the past, including castles, necropolises, bridges, monasteries, and more.
While Bosnia and Herzegovina does not produce a significant quantity of wine, it does produce some very good wine.
The two most common varieties of wine are Žilavka and Blatina and you can visit a number of wineries in beautiful locations to sample and buy some Bosnian (I should probably say Herzegovinian wine).
This last section is a short one and leans on imagination and faith for its legitimacy.
There are a few locations in Bosnia which are open to debate: a giant pyramid, supposdely the largest in the world; a pilgramige site where the Virgin Mary is said to have appeared on occassion; and Europe's largest stone sphere.
Then, less up for debate, there are herds of wild horses which roam near Livno.