Currently in our Abu Dhabi office, live down the road in Dubai, but about to relocate to Italy.
Accommodation is considerably cheaper in Dubai than Abu Dhabi for the same sort of quality, especially if you want to be near the centre, but it is a reasonable drive each way.
There is a reasonable amount of biking in Dubai, both road and mountain, but don't know of much which goes on in Abu Dhabi. Friday morning club rides with the Dubai Roadsters have ensured that I don't waste the weekends with lie ins (5:30 am ride start )
All the mountain biking has been pretty much on the Dubai/Oman border, where it stops being sandy, and starts getting rocky and mountainous. There is an active MTB club with a small but keen core group. I've mainly been riding at night, as it's too hot during the summer to be out during the day for too long, so make sure you have a good set of lights.
There is a good bike shop in Dubai, although not cheap, stocks a good range of stuff.
Can't be of much help for living in Abu Dhabi, but hope that's useful.
Feel free to drop me an email directly if you want to pick my (limited) brains further