Salem's central sights are fairly spread out but manageable by auto-rickshaw. Autos are metered in theory but bargaining is standard practice — agree on a price before you get in. Share autos run fixed routes across the city at low cost, though figuring out the routes takes some local knowledge.
City buses cover most areas including the route to the base of the Yercaud road (Yercaud Ghat Road), but for the hill station itself you need a bus from the SETC bus stand near the railway station, or a taxi. Taxis for the Yercaud trip cost around ₹400–600 one-way depending on negotiation; shared jeeps also make the run and are much cheaper.
The city centre around Four Roads and Shevapet is walkable once you are in it. The fort area and museum are a short auto ride from the railway station.