I was in Abu Dhabi some months ago, and looked for fishing opportunities in the area. You're right - very limited. Despite the beautiful waters it seems that nobody goes fishing. Inquiring locally I found that it is pretty fished out (verified?); not much there. I was kinda disappointed. Better luck if you could make a weekend in Oman from what I remember. Diving is pretty good, though.
Lots of other things to do though - desert safaris, dinner cruises, formula 1, drive around in a rented ferrari...
Would be interested to hear if you come up with anything.