Meaux is a compact city and most visitors on a day trip will need nothing more than their feet. The station, the cathedral, the market square, the Musée Bossuet, and the Marne riverbank form a walkable cluster of well under a kilometre across — the whole historic core can be covered comfortably on foot in a morning.
On foot is the right way to experience the old town. The streets around the cathedral and bishop's palace are narrow and medieval in scale; driving them serves no purpose.
The Musée de la Grande Guerre is the main exception: it sits on the eastern edge of Meaux, about two kilometres from the station, on the road toward Verdun. The walk takes about twenty-five minutes. Alternatively, town buses (run by SITUS, the local network) connect the station to the museum stop. A taxi from the station costs a few euros and takes five minutes.
By bicycle, the flat Marne valley terrain makes cycling easy. Vélos Bleus, Meaux's municipal bike-share scheme, has stations near the station and in the town centre, with modest hourly rates. The towpath along the Marne is traffic-free and can be followed east toward Trilport or west toward the confluence with the Grand Morin.
By car within the town is unnecessary and parking in the historic centre is limited. Use one of the free car parks on the periphery if you arrive by car and walk in.