Those in the UAE should know there are not many places to get things notarized like in the US or Europe, where you can go to banks or private businesses to get this done. In the UAE you basically have two options: your embassy or the UAE courts.
Essentially if the document mainly has to do with the UAE, then there's a chance the courts will notary or attest it for varying fees (i.e. business contracts or business creation, UAE immigration documents, marraiges or births that took place in the UAE, etc). However, if the document is not 100% UAE related you may be told to go to your embassy to get it notarized. That usually requires an appointment, a fair amount of waiting time and some hefty fees for simple notary services.
If there is a chance you will need something notarized while here, my advice is to try to do this from overseas. I also understand why getting documents or marraiges attested from overseas is recommended by every site I visited... The bureaucracy here can be fairly intimidating and you will have enough stuff going on right after arriving...
The list for Abu Dhabi is above and Dubai here.
I just found a list ofnotaries, solicitors and translators from the UK embassy, which covers all the Emirates. Thank you UK government!