Surprisingly for the capital of the largest Muslim country in the world, the number of Arab or Middle Eastern restaurants in Jakarta is quite low. I've counted about 25 of them, and I've tried 15. It may seems like a lot, but since Jakarta is so spread, you're not likely to have more than just a few near where you live.
The good thing is that within these, most of them are decent and affordable. In particular, I advise you to try one of the Yemeni restaurants which offer the best value-for-money and the most authenticity.
As of October 2011, here is my Top 10 for my favourite Arab or Middle Eastern restaurants in Jakarta (you can click on the link to read my personal review):
1) Maroush (Morrocan Restaurant)
2) Al Nafoura (Lebanese)
3) Anatolia (Turkish)
4) Samarra (Middle-east)
5) Al-Jazeerah (Yemeni)
6) Turkuaz (Turkish)
7) Sinbad (Syrian/Yemeni) - Review not posted yet, the restaurant is located Jl. K.S. Tubun Raya No. 2 in Slipi (Tel: +62-21 530 8366)
8) Beirut Lebanon (Lebanese)
9) Hadramout (Yemeni)
10) Diritna (Lebanese)
You may see more reviews of Arab restaurants in Jakarta on this blog by clicking on the label "Middle East".