The weather window I would choose
Belgrade is strongest when daylight walks and evenings both work.
- May to June works for warm days before heavier heat.
- September keeps the evening atmosphere without peak summer pressure.
- October is good if you pack for cooler nights.
For a first trip, I would choose May, June, September, or early October. Those months give enough warmth for long central walks and enough evening comfort for dinner, cafes, and river-side plans.
High summer can still be fun, especially at night, but the daytime city can feel heavier. Winter can work too, but the trip needs more warm interiors and fewer long exposed walks.