Gitega is a compact town and most of the main sights — the National Museum, Christ the King Cathedral, and the central market — are within walking distance of each other. The town centre can be explored on foot in an hour or two.
Motorcycle taxis (moto-taxis) are the standard form of local transport and are inexpensive. Agree on the fare before getting on. They can take you to the National Museum (about 2 kilometres from the centre), the cathedral, and other points too far to walk comfortably.
A taxi can be hired for a half-day to cover the main attractions including the royal drummers' site, which is outside the town centre. Arrange this through your guesthouse or through local contacts. Fuel and driver costs in Burundi are modest by regional standards.