>> Any idea of the cost and time needed?

It's 120km from AUH to Downtown Dubai. Somewhere between 250-300 dhs on the meter and around 90 mins depending on traffic. Airport taxis are nice Merc minivans. Uber is still discouraged from airport pickups, I believe.

As I commented above, have you checked fares to DWC and SHJ ? Sharjah borders Dubai and it's only 20 mins away outside the rush hour.

Clearly I prefer Abu Dhabi but everybody needs to see Dubai before they die