Sofia is small enough to walk. The historic core, from Alexander Nevsky to the Palace of Culture, is barely a kilometre across; the central pedestrian streets — Vitosha Boulevard and Graf Ignatiev — are where most visitors spend their time.
Metro. Four lines, cheap, clean, and the easiest way to cover longer distances. M4 connects the airport to the centre; M2 runs north–south past the train station; M3 reaches Lozenets and the university. Buy a single-ride ticket or a 24-hour pass from machines at any station.
Trams and buses cover everywhere the metro does not. The same tickets work across the network. Validate on board — fines for unvalidated tickets are routinely enforced on tourists.
Taxis are cheap by Western European standards but the unregulated airport touts are a long-running scam. Stick to OK Supertrans (yellow cabs, clearly marked), or use Yellow Taxi or Bolt via the app. Confirm the meter is running before you start.
Vitosha mountain is reached by the No. 64 or 66 bus to Simeonovo, then the gondola lift up to Aleko. The whole trip from the centre takes about an hour.