I'll add another vote for Ivans on the cliffs. Its my top spot on the cliffs for dinner. Many more good choices but Ivans is top shelf.
If you want to stick to the beach you might want to take a look at Kuyaba. It's one of the more popular places for dinner, I try to stop in for at least a snack and drink every trip. Have cool rope swing bar stools. There are also a number of small more "rustic" places all along the the beach. Been to many of them but at the moment can't remember which were hits and which not so much. Also.. theres Cosmos, its a short walk (to the right facing the water) from CSA. Good, authentic Jamaican food. Their Conch soup and festival(fried break type snack) are great for lunch.
Love the food at CSA but there is also a lot of good food to be had all over Negril.