At the end of a trip to Oman, I have just spent a few days in the Dubai area, so first I'll recommend the website by Tommy Pedersen, it really covers everything
http://www.tommypedersen.com/UAE-sites.htm
The best site in Dubai is the the Pivot Fields, really super - had 52 White-tailed Plovers there, plus all the usuals. Also a vagrant Brown Shrike there (with Isabelline Shrikes too) and a vagrant Moustached Warbler. Near the Brown Shrike I found a Grey Hypocolius, apparently the 2nd for the locality.
Next, the nearby Wimpy Pools, rather naff at first glance, held vagrant Streak-throated Swallow, etc, but I didn't bother. Safa Park currenty has a Red-flanked Bluetail, the first ever for Arabia.
In the centre of Dubai, the Ra's al-Khor Wildlife Sanctuary was okay, but everything I swa there I had seen in far better numbers elsewhere in Oman and near the Dreamland flats (see below), so only visited once. It is very good however for Great Spotted Eagle if you haven't seen this bird - I saw about five here. Mangrove hide is the best, the other one had almost nothing.
For U.A.E. specialities, trips beyond Dubai could incude Ghantoot, about 60 km towards Abu Dhabi - Cream-coloured Coursers are guaranteed (I saw 47 on the polo club grasses) and Grey Hypocolius is usual there - up to 12 this year (but I didn't see here). In the other direction, the big tidal flats at 'Dreamland', mentioned on the above website were interesting - had 520 Crab Plovers there, plus three Great Knot on one visit, lots f Terek Sandpipers and Greater and Lesser Sand Plovers, etc.
Be ready for a shock - Dubai and even more so Ras at Khamah (if you have the misfortune to go there) are amongst the most unattractive places I have ever been to! But the birds are good, so shouldn't complain.
If you need any further detail, feel free to ask.