Solo is compact enough that most of the central sights can be reached on foot or by short becak (cycle rickshaw) ride. The main palace area, Pasar Klewer, Fort Vastenburg, and Pasar Gede are all within walking distance of each other.
The city operates a Trans Solo Batik bus rapid transit system along Jalan Slamet Riyadi, connecting the main railway station with the Sriwedari area and beyond. Tickets are cheap. Online ride-hailing apps (Gojek, Grab) are widely available for motorbike taxi or car services, which is the quickest way to reach Laweyan or the Sheikh Zayed Mosque.
Becak are still common in the old palace quarter and are a pleasant way to explore the lanes around Baluwarti if you negotiate a rate for an hour rather than paying per journey.