Truly near the Convention Center is tough. The BEST places near there are Le Pigeon, Biwa, Simpatica (not a normal restaurant), and Clarklewis. But these aren't exactly quiet. (Well, Biwa hasn't been noisy when I've been there, but that might be because it wasn't busy.) In fact, they can be oppressively noisy at times, though the food is very good at all, high quality, but not overly expensive (mostly under $20 for entrees).
You could head up to a local midscale chain like Stanford's or Newport Bay near the Lloyd Center Mall. Competent food.
However, the Convention Center is very near the Max line which gives you easy, quick access to downtown. You could try Karam, Mama Mia's, or Mother's for places very close to the Max that will give you good food at reasonable prices. These would probably be less noisy than the above, as well.