Hi Heather! I remember eating out when my son was that age -- my husband and I would have to take turns walking him around outside while the other ate; I wondered if we'd ever be able to eat a meal in a restaurant together again! (Thankfully, this stage does pass!)
All of the restaurants at Walt Disney World (with the exception of the adults-only Victoria and Albert's) welcome children and will provide you with crayons and a coloring page to help keep your little one entertained. Generally, the character meals and the buffets are loud and full of activity -- it's unlikely your 18-month-old would be noisier than the other patrons, and the bustle of the diners going to the buffet and the characters passing by will likely keep him occupied. Consider Chef Mickey's, The Crystal Palace, Hollywood & Vine, Tusker House or Boma. The Signature restaurants, on the other hand, are much quieter. While these finer restaurants certainly welcome children, I, like you, am sensitive to not interfering with the enjoyment of other diners, and if you feel the stress of trying to keep him quiet would ruin your meal in these more upscale restaurants, you may want to avoid them for now.
In addition to buffets and character meals, I think your son would be so mesmerized by the activities in these restaurants that he'll forget he doesn't like to sit nicely :
- 'Ohana, which is loud and has activities, such as limbo and coconut races that allow little ones to get up from the table and burn some energy
- Coral Reef, where you can watch sharks and tropical fish swim by in the giant aquarium
- Sci-Fi Dine-In, where you eat your meal in a "car" and watch campy drive-in movies while you dine
- Teppan Edo, where the hibachi chef cooks your Japanese food tableside
Hope you have a magical vacation, full of quiet meals!