Central Kumasi — Adum, the Cultural Centre, the Manhyia Palace, the cathedrals — is walkable in a single morning, though the heat and traffic can be tiring. For longer hops, shared taxis (drop-offs along fixed routes) and tro-tros (minibuses) leave from Kejetia and cost very little.
For an unfamiliar destination, hail a dropping taxi — a private hire — and agree the fare before you get in. Uber and Bolt both operate in Kumasi now and are usually cheaper than the negotiated price, particularly for trips to the airport or outskirts.
The Kejetia roundabout is the orienting landmark: nearly every taxi driver in the city knows where it is, and most cross-town routes pass through it.