What is the correct term for a crag that has already been set up for climbing?
These are usually referred to “bolted” routes or “sport” routes. Sport climbing is either top rope or lead where there are bolted anchors (and sometimes bolts for lead protection) in contrast to Trad routes which have no bolted ancors or no bolted protection. As for knowing whether any of your local routes are set up as sport routes, get a guide book – it will show each bolt (usually as an “x” on the route diagram) and will indicate what gear is needed.