Question

When the body receives stimuli, which structure typically processes the stimuli?

Answer 1

The stimuli are processed by the brain. There are specialized regions and cortical networks of neurons that work together in synchrony and harmony which enable you to perceive and process stimuli. 

When we first receive stimuli, our sensory nerve cells transmit these to the centres responsible for sensory stimuli decoding, when these are sufficiently decoded and we're aware of what we've perceived either through our eyes or our hearing for example, we then take action with our motor nerve cells which command our limbs; hands, legs, and other muscles around the body.

Meninges are the only structures here which don't really play a role in processing as they are more of a defensive structure for the brain. 

Answer 2

The brain is what processes the stimuli.

Sensory nerve cells are what first send the pain signals to the brain, motor nerve cells are the cells that receive the signal for the muscle to move or react to the stimuli and the meninges are the protective covering of the brain.