When I arrived by bus, next to the train station, there was only one money exchange shop located in the post office. The communist era service ethos had me wait for a while even when there were no other customers. Once I handed over my cash, they were inspected intensely and any note with too many folds or wrinkles were handed back to me... enough so that I ended up going back to the bus station to use the only ATM in the area. So basically if you arrive at an odd time with the post shop is closed or the ATM doesn't work with your card, then it will be a walk to the city. Most of the accommodation is on the opposite end of town a couple kilometers away. Overall, I didn't find Sarajevo a very traveler-friendly place, but there are some places of historical significance to visit. The most recent war has ended about 20 years ago but there are plenty of bullet and shell ridden buildings around town. There are museums that go through the history of WWI, which was started based on the Archduke Ferdinand who was assassinated in Sarajevo (there is another small museum dedicated to only that, located next to where he was murdered). Other sites include old mosques, old market and a nice cobblestone streets of the old town to wander around in. After the war, many of the Christians have moved to East Sarajevo and there are still some tensions that remain.
The 103 trolleybus is handy to get to the bus station in East Sarajevo which has the most connections to Belgrade. Just take it to the final stop and you will see the bus station a couple hundred meters ahead on the left. There was only one bus from the main bus station (next to the train station) departing at 6am, but the other station in East Sarajevo has 5 per day.