Msemo (aka Southern Cross)
Shangani
This is the only real option for western food in town. It's by the sea and is a nice place to while away the afternoon. During the day it's about a 20 minute walk from the center of town, after dark it's probably better to go by taxi / tuktuk bajaji / motorbike pikipiki.
Bima
This is an area of town where there are a cluster of bars that gets a bit of an atmosphere in the evening.