Just came back from a whirlwind trip that included a few restaurant meals worth mentioning, for better and for worse.
In western Amman, we ate at a Lebanese restaurant, Diwan Al Sultan Ibrahim. It was delicious, from mezzes to entrees. Highly recommend the lamb chops, and anything with eggplant. Had lunch at the casual Books@Cafe, on Rainbow Street. Nice hangout, but the food is a bit over-rated and very westernized/student oriented. The lentil soup was delicious, though. Sidenote: I found out after our trip that a friend had recently been in Amman, and told me that Fakhr el-Din, behind the Iraq embassy , is amazing. Also, Rheem (a shwarma joint) was just written up in the NY Times.
In Aqaba, had only one dinner - at Hayat Zaman. Again, after reading elsewhere that it was the best in town, we were disappointed. The maitre d' recommended the fish platter (shrimp, squid, fish filets), which my husband ordered. It should have been dead-simple, sauteed or grilled with lemon. It was dead-simple, and dead. The shrimp were old and tired, the squid white rubber rings, the filets greasy tasteless. Pathetic. I tried the Jordanian national dish, Mansaf. Sort of like lamb stew cooked in a watery yogurt., with plain rice on the side. The versions I've since seen (googled) look quite a bit more interesting, with herbs and/or nuts in the rice. The restaurant on the whole had a very pleasant atmosphere, seemed frequented by locals, and service was fine. I'd try it again, but with caveats - avoid the seafood.
Petra, again only one dinner, and the only real options here are at the hotels (or so I've read). We stayed at the Crowne Plaza, and had the dinner buffet. The salads were excellent, and very varied, the meats acceptable. The fish looked sad, and I couldn't bring myself to try here.
Wish I had more to report on, but between large breakfasts (generally wonderful, even at simple hotels) and on-the-go travel days, didn't experience as much local food as I'd have liked.