The most basic adaptation to faster neural functioning is the ability to precipitate metals. Once a life-form has the ability to precipitate metals and build metal structures within its body, it is not a particularly great evolutionary step to neurons with metal axons.
If we have a metal axon with a seperate metal core, like a biologically-created coaxial cable, we've stepped up the speed of neural transmission from hundreds of metres per second to near light-speed. The main delay will then be the time it takes for a neuron to depolarise and the wave of depolarisation to travel to the metal axon. From there, the voltage differential will propagate at light speed to the far end of the axon where the dendrites will depolarise at the slow speed, and transmit their signal to the next neuron via molecular diffusion of neurotransmitters across the neural gap.
It might seem that a metal axon would be rigid, and could not bend, but this axon would be many times thinner than a hair. When metals are that thin, they bend very easily. They would be no more fragile than common myelinated neurons.
As to what metal might be used... silver would provide the lowest electrical resistance, followed by gold and copper. However, the scarcity of silver and gold might mean that copper is used for no other reason than its relatively low resistance and relatively high availability.
So... with metal axons, an organism could be hundreds or thousands of metres long, yet still have the same speed of neural transmission as a much smaller creature.
Since there is some misunderstanding as to how this works, I'll explain further:
A regular neuron's cell wall has a charge across it. The cell wall is a poor conductor. Within the cell wall are voltage-sensitive ion gates. When neural junction activation causes sufficient depolarisation as a field effect around the junction, the voltage-sensitive gates open briefly, sending a wave of depolarisation across the cell membrane. Since the gates aren't particularly fast, and since the field effect of the charge is limited, this limits the transmission speed.
Now, if we were to precipitate metals inside and outside the cell membrane, the metal layers, being conductive, would transmit the voltage along their mass at lightspeed. In effect, there would be a continuous metal fibre inside the axon, and a continuous metal sheath would replace the periodic myelin sheath.
So, instead of a long axon with slow gates and perhaps myelin to make the axon a little faster, we'd have in effect a cellular-scale coaxial cable, where the insulating layer between the conductors would be the cell membrane. As I have said, this will transmit the voltage differential from one end of the axon to the other at lightspeed, from where the usual ion gate depolarisation effect continues.