I am in Fujairah and am planning to shift to Qatar in a few months. Fujairah is a laid back town with hardly any traffic, OK shopping and 2 decent CBSE schools and a few GCSE schools and a British school too. The best thing is that it is hardly a hour away from Sharjah and a hour and half from Dubai, so you can go to Dubai or Sharjah any time you need and then come back to the quiet of Fujairah.
The cost of housing is comparatively less compared to Qatar, but at the moment the demand is more than the supply due to shortage of electricity for completed houses. If you get a better career deal in Fujairah then move. The rest of shopping and cost of living is the same as in Qatar
Anand