cevapcici is the national dish there, a kind of grilled minced meat made from beef or mixed beef and lamb with flatbread and onion . But my real favourite is the streetfood burek/börek, a baked filled pastry, which is also very popular all over the Balkans and Turkey, but IMO the Bosnian one is the best version. I prefer the ones filled with meat but there are also non-meat variants. Drink yoghurt or the Turkish ayran (a yoghurt based drink) with them. They are extremely filling.
I'm writing these from memories as i was there years ago, so there could be some changes...
Sarajevo is a majority muslim city, but don't be surprised, practicing people are a minority (in the country-side people can be more observing, i don't know), it is mostly just a cultural identity. Giving muslim names, celebrating the bayrams/eids... they won't eat pork at all, it is a taboo, but many consume alcohol just like in other European countries and only a small minority of women covered themselves... Mosques were quite full during the Friday prayer, but can't say this about other times. The old center has many historic mosques, there are big ones, like the most famous Gazi Husrev beg mosque, but my personal favourites were the smaller old mahalle (neighborhood) masjids, they were also nicely renovated.
in the modern communist and post communist parts as i recall i saw few mosques, though i remember seeing two modern big mosques from the tramway in the modern parts of the city, built from foreign finance (a Saudi and an Indonesian).
There is also a really old orthodox christian church, an old sephardic synagogue (now museum?) and 1-2 19th early 20th century catholic churches in the downtown.
The martyrs cemetery of the recent war is also very close to the center, and it is also the place where Alija Izetbegovic (first president of independent Bosnia-Herzegovina) was buried. Visit it and say a dua if you are there.
And of course don't miss the site at the Latin Bridge, (an Ottoman era bridge) where Archduke Franz Ferdinand was assassinated in 1914, causing the outbreak of world war 1.
I was also there during the summer, but they still take pride of the 1984 winter olympics being held there, so i assume there can also be some winter sport opportunities.
I went there by train, but no matter if you go by train or by plane, both way very simple and easy to get to the city center.
So far Bursa was my favourite city in Turkey if i consider things like historical heritage, natural beauty and livability combined, but unfortunetly i haven't been to too many cities in Turkey to make big comparisons.