The musika or people's market is a fun place to go to buy fruit, vegetables and crafts. It is located in Sabkuva - probably Mutare's most 'notorious' high density suburb. The part of the market where rural people sell their produce directly is only open until 11:00 am each day. After this time you can still shop at a covered market where you'll pay less than you would at the open air stalls in town but more than you will in the direct sale market.
I suppose you could take a taxi to the market but that would be very expensive (well, in Zimbabwean terms - not in tourist terms). For the real experience I would suggest taking a commuter minibus - unfortunately given fuel shortages this might be tricky. Your best bet is to go to the bus boarding area (near the toilets in Meikles park) and ask around. You could walk but it is about an hour's walk from town.
To get yourself a good map of Mutare go to the Manicaland Publicity Association office (Meikles Park) where they have them for sale. Once you're done at the vegetable market you can head back towards the covered market near the TM supermarket for crafts or head across the street to the flea market (which is near the swimming pool) to look at clothes and shoes.
A lovely region of mild climate, always green and peaceful (except for the fact the armed bandits had some basis here and there...). It's better to hire a car and wander around....