Hi Melissa,
My daughter does not like the noise of the fireworks so I can sympathize with your son. We usually do the dining to avoid the noise.
Off the top of my head I can not think of any indoor spots without dining but maybe these suggestions will help. First, you can buy earplugs for your son to use. You can get them at most stores and this should reduce or eliminate the noise. You could also use headphones and play music over the noise.
For Magic Kingdom, try viewing the fireworks from the beaches of the Grand Floridian or the Polynesian. Or stand on the walkway between the Contemporary and Bay Lake Towers. If you are really lucky, you might be able to sit on the monorail and watch them.
For Epcot, stand by the big fountain in Future World. The fountain drowns out a lot of noise and it is closer to the bus and transportation home.
Wishing you a magical vacation!
Beth