Yas is 15 minutes from AUH, 45 minutes from the Marina end of Dubai and probably a good hour to DXB. I agree with mecabq: a week is a long time to spend on a desert island with one golf course, one tourism attraction and 5 hotels. I'm not sure when the new Yas beach will be open - but the Corniche beach is good on the main Abu Dhabi island (a bit of a trek from Yas though).
You could spend a night at Qasr al Sarab too.