After you have enjoyed the old market Baščaršija in Sarajevo the next area to check out would be the modern downtown with its gov't buildings and the major museums.
It's easy to get there on the tram, just show the driver some change and he'll take whatever crazily cheap BAM fare it needs. A handful of stops later and you're at the various history and science museums -- don't jaywalk to/from the trams because the street traffic is moving quickly. Note that with the last change of administration, the trams are their traditional dark blue again, after the previous gov't had let them be plastered with advertising. Tradition before profits, da?
But maybe you want to take the time to walk here so that you can see the remnants and memorials of the nineties along Sniper Alley, and browse the revivified book fair and street life. Keep an eye out for Sarajevo Roses
Behind the history museum you will find a family-friendly beer garden called Cafe Tito.
https://www.facebook.com/profile.php?id=100064088611326
This is today's Sarajevo: hip, friendly groups and families hanging out in a garden setting, or crowded together inside surrounded by decor that idolizes Josip Tito -- medals, memorabilia, news clippings, signposts, portraits. It's part kitsch, part reliquary.
The garden includes a sandlot for kids with the most remarkable playground equipment that I have ever seen: scrap weapons systems and vehicles from the Yugoslav military. Jeeps, tanks, cannon carriages, an armored rail car, all being crawled over by tykes playing antifa instead of cowboys and indians. The parents are kibbitzing over enormous glasses of beer with their designer pets (mostly dogs) splayed underfoot.
Cafe Tito is the active break from your museum visits -- the quiet break is not many meters back eastward in the courtyard of the Nat'l Museum where there is a peaceful botanical garden (Botanički vrt).
In-between the two is an outdoor event space called Stage Park, known as "a cultural epicenter" of Novo Sarajevo.
https://voicemarks.app/places/bosnia-and-herzegovina/sarajevo/novo-sarajevo/stage-park/
When I happened by during my early June visit there was a DJ hosting an after-party for a big bicycle ride / fundraiser that had happened that morning. Later on the bus some of our tour group said they had spotted a lot of bicycles going by that morning and wondered what it was; this was it.
Keep in mind, though: Smoking. Smoking. Smoking. Very hard to find a spot where you're not being exposed to smoking and vaping. Grrrrr ....