The old city centre is compact and almost entirely car-free — walking is the main way to get around. From the station, the Dom Tower is a fifteen-minute walk through the Hoog Catharijne mall.
Cycling is how locals move around Utrecht, and the infrastructure is exceptional even by Dutch standards. The Stationsplein has the world's largest bicycle parking garage (12,500 spaces) right beneath the station. OV-fiets bike rental is available at Utrecht Centraal and at several other stations in the city.
For the Rietveld Schröder House or the Castellum Hoge Woerd, take a local bus or hire a bike — both are 20–30 minutes from the centre. The RET city bus network is run by U-OV; a day pass or OV-chipkaart covers all buses.