>> My goal is to get to Abu Dhabi three days before I depart so I can spend some time exploring.
Aha @:-)
Be aware that AUH is a good 20 miles outside the city, en route *from* Dubai. So if you take transportation to AUH, you'll then need to get into the city. Unless you're staying near the airport of course (e.g. Yas, Al Raha). Add another $10 to the cab fare.
I'm a great supporter of the public transport system, and the bus between the cities is very good -- cheap, fast, frequent, reclining seats, a/c, free wifi, space for bags, etc. It goes from centre to centre and you don't have to chat to the driver about cricket for an hour
Google maps has schedules: look for service E100 or E101. Then a quick $3-4 taxi from the AD bus station to your hotel.
Maybe hold off on this decision until you know where you'll be staying in each city; they're both pretty sprawled out now and much will depend on your precise origin and destination points.