Tomsk is walkable in its historic centre. The wooden architecture district, Resurrection Hill, the university quarter, and the main Lenin Square are all within comfortable walking distance of each other. The city is flat enough that there are no real hills to contend with beyond the climb to Resurrection Hill itself.
The city has trams, trolleybuses, and buses covering the wider urban area, all running on the standard Russian flat-fare system. Taxis are cheap by Western standards and widely available — in practice most visitors use taxis or rideshare apps (Yandex.Taxi works well in Tomsk) for any journey beyond the historic core.
In winter, walking requires proper footwear — the pavements are icy and snow-covered for months. Snow boots with grip are essential. The cold itself is manageable if you are dressed for it: multiple layers, a proper coat, hat, gloves, and warm boots. The wooden architecture is best explored by walking, so prepare accordingly.