The centre of Eskişehir is small, flat, and easily walkable: the train station, the Porsuk riverside, the central mosques, and the foot of Odunpazarı are all within fifteen minutes of one another. For the climb up into Odunpazarı, the buses and trams give your legs a break, though the walk is not too steep.
The city's tram network (Estram) is excellent — modern, frequent, cheap — and connects the train station, the universities to the west, and the otogar. Buy a contactless EsKart from any kiosk for tram and bus journeys. Taxis are cheap and metered. For longer distances out to Sazova Park, a tram is fine; for Phrygian Valley day trips, a hire car is best.