I would suggest the Old Airpot road/ Madinat Kalifa for accommodation. The area just behind family Food Center( the entire plot) is quite a good place as the population consist of 80-90% families.

The rents are quite reasonable ranging from QR4000-8500.
The best part is, it is close to corniche,FFC/lulu and many other fast food eat outs.
Good Luck!