The historic centre of Toluca is small and walkable — the Cosmovitral, the cathedral, the Portales, the main museums, and the market are all within ten minutes of each other on foot. For sites outside the centre (Centro Cultural Mexiquense, Calixtlahuaca, Teotenango, Nevado de Toluca), a taxi or Uber is easiest. Uber works well in the city; Didi is the other main app.
City buses cover the urban area but are slow and not well signed for visitors. The El Insurgente commuter train serves a useful set of stations along the southern edge of the metropolitan area. If you are planning a trip out to the Nevado de Toluca volcano, the easiest option is to hire a car with driver for half a day — most hotels can arrange this.