Not sure when you are planning on coming, but if its in the next couple of months then you need to know that its still very hot during the day - around 48 degrees - and humid - today was 50% at 9am! We are also in the middle of Ramadan which is expected to finish around 10 September. This means no eating or drinking in public during this time and lots of smaller shops shut in the afternoon, but open again later. Also, some of the hotels are not serving alcohol and you may find it slightly harder to find a taxi during prayer times.
Once the Eid Holiday is called - at the end of Ramadan - then Abu Dhabi will be busy for a few days, as will lots of other holiday destinations within the Middle East. This may impact on what you decide to do.
Abu Dhabi Culture and Heritage lists various activities and sites http://www.adach.ae/en/
Abu Dhabi Tourism Authority http://www.abudhabitourism.ae/en/Default.aspx
Must sees for two days would be:
Free public beach - plus there are some areas that you can pay a small amount and get a sun lounger, towel, umbrella etc. located on the corniche but the sea is hot - its like swimming in soup!
Sheikh Zayed Grand Mosque - fabulous mosque which is a must see and has well organised tours available http://www.abudhabitourism.ae/en/portal/zayed.mosque.aspx
Yas Island to see the F1 circuit
Friday Brunch at one of the hotels if its not Ramadan
Trip out into the desert with shisha and a traditional dinner organised by one of the 4x4 groups which can be arranged via a hotel or a lot of people say Arabian Adventures are good http://www.arabian-adventures.com/
Shisha - try Special Cafe which has three locations on the corniche, or go to a swish shisha tent at one of the hotels such as the Shangri-La or Emirates Palace
And if you have any left over time:
Emirates National Car Museum has some corkers in it http://www.enam.ae/ver4/index.php
Jebel Hafyeet in Al Ain - about two hours away is great - up a mountain, wonderful views, cool breeze!
Shopping - lots of malls
Trip to a camel farm! almost 8 years ago