Taxis can be difficult to find in Mtwara; you'll mostly need to rely on bajaji (tuk-tuks), which are everywhere. Bajaji 'stands' are at the bus stand, and near the CCM building at the intersection of Tanu and Uhuru roads. To and from the airport (6km southeast of the main roundabout) expect to pay about Tsh10,000 for a taxi and about half that for a bajaji. The cost for trips around town in a bajaji is Tsh1000 to Tsh2000 (Tsh3000 from the centre to Shangani).
There are a few dalla-dallas running along Tanu Rd to and from the bus stand.
To get to nearby Msangamkuu Peninsula, there is a ferry that runs daily between sunrise and sunset (Tsh300, about 15 minutes).