I do not own or do any private flying. I don't think this is yet "free" here. I believe the Northern Emirates will allow you to do so. On your days off, drive north and go to Ras Al Khaimah, Ajman or even Umm Al Quwain. I know there are 2 schools (
).
Having written the above, start by calling +971
7 244 8541. It's the local ATC number and they will help you get some information where to go next. Also try this site:
http://www.uaeflyingclubs.com/ Good luck!