Tamale runs on motorbike taxis, locally called motokings. They are everywhere, they are cheap, and they will get you almost anywhere in the city for a few Ghana cedis. Agree on the price before you get on — GHS 3-8 covers most urban journeys. It is the fastest way to cross the city and the way most locals travel.
Shared taxis and tro-tros follow fixed routes and are even cheaper, though slower and often crowded. Private taxis can be negotiated for longer trips or if you want to make several stops; agree the fare in advance. For the journey to Mole National Park, hiring a private car or joining a shared arrangement through your guesthouse is the most practical option — the road is rough in places and the distance is too far for public transport if you want any flexibility.
Tamale itself is fairly compact and the market area is walkable from most guesthouses, though the heat makes long walks uncomfortable in the middle of the day. The city is predominantly flat, which helps.