Market (soko)
The market is the best place to pick up local goods from food and clothes to traditional medicines. Generally bargaining is not expected and the same price is given to locals and tourists alike.
Hendricks Family
The Hendricks family are the most famous of the makonde carvers still in Mtwara. Their work is available in town, or you can visit their carving workshop in Ziwani village just outside Mtwara. It's easiest to reach by vehicle, head out of Mtwara on the airport road and take the turn off for Mozambique / Mnazi Bay Marine park. It's a couple of miles down that road. They are most famous for their 'cloud' carvings which are carved out of a single piece of wood and make a cage out of lots of interconnected branches.
Gift shop
The gift shop attached to the hotel/restaurant has a decent range of local crafts.
Carving Stand
A small stand selling a range of Makonde carvings. If you're a good negotiator this is the best value place to buy your Makonde carvings.
Ray shop
For general supplies there are a bunch of shops at the Bima made out of old shipping containers. They all contain fairly similar things but Ray Shop usually has the best selection.
ADEA
An arts and crafts cooperative producing high quality handicrafts, mostly based around tingatinga painting.
Makonde Mini Mart
A little more ex-pat orientated than the container shops at the Bima. If you can't find what you're looking for there this is probably the best bet.