actually there is really nothing to do in AD except visiting Sheikh Zayed Mosque - the biggest and the only opened to non-Muslims in UAE. but it's opened till 1 p.m. or somewhat

Depends on what sort of activities you wish to exhaust your day with. I would suggest Abu Dhabi Mall and Marina Mall if you are interested in shopping. Rest your feet and grab a bite at Rodeo Grill (at Beach Rotana Hotel) or Prego's where they serve great Italian food. If you are a woman, I wouldn't recommend visiting any restaurant (in a hotel) at night since they are crowded with vultures looking to ride you (pardon my crassness =P). For fun and adventure, check out Yas Island which has the Ferrari themed amusement park. The world's fastest roller coaster that enthralled Fernando Alonso! Defenitely not for the faint hearted! If you are looking for culture and tranquility, check out the Corniche, the Khalifa park and the Abu Dhabi Cultural Centre. Helicopter and desert safari tours should be booked in advance for a total tourist experience. But since you are an impromptu traveler, you can stick to my advice above =) Have fun and as they say in Arabic, Ahlan Wa Sahlan; enjoy your stay!

Walk around one day, then book a desert safari for a whole day, or better yet an overnight desert safari...get out and experience the desert! You can head to Hatta on a tour as well and go camel trekking or other active things. Definitely don't spend the whole time in the city.

You can see Yas Island. Yas Marian circuit is worth visiting as well. You can take a boat ride in the gulf as well

visit the emirat palas and the Abu Dhabi mall for sure