Abu Dhabi Attractions

Sheikh Zayed Mosque ( map ) is beautiful mosque that's a must-see in Abu Dhabi, even if you're not religious. It's free to visit, but make sure you check their visiting hours before going. At night it's lit up and absolutely breath-taking.
Emirates Palace ( map ) is the second most expensive hotel ever built with a nice fountain outside. You can even find a vending machine for gold here! Although I only walked around, you can have high tea here.
Ferrari World ( map ) is an amusement park on Yas Island. I didn't actually go inside the park, but it's supposed to have the world's fastest roller coaster. Of course there are all sorts of souvenirs you can buy at the gift shop without going inside. Also, there are many posh hotels on Yas Island where you can hang out and go for a bite to eat.
Heritage Village ( map ) is an interesting way to spend an afternoon. There isn't an awful lot of stuff in there, but it's free and a pleasant place to walk through, especially if you're shopping at the nearby Marina Mall. Plus, there's a nice stretch of beach there.
Iranian Souk in Al Meena ( map ) is an open market near the water selling exotic handicrafts. There weren't very many people around when I visited, probably because this is not a fancy place. While it may not be a place you must drop by, you might find some interesting souvenirs/housewares here.
Masdar City ( map ) is a campus where you can ride a completely automatic driverless robot car for free. Other than that, it's not really a place for tourists.