You might try looking in Najma or Mansoura which are both quite close to the airport and have quite a few newer buildings. While it looks like chaos in the interior streets at certain times of day it is an easy area to get a taxi and walk to the local corner store and small restaurants. There is a fair supermarket (Al Meera) in Mansoura and a Dasman Hypermarket and Family Food Centre close to the airport.

HTH