The speed of action potential conduction is faster in larger diameter axons because there is less resistance to ion movement along the length of the axon.
One way to think about this is that a larger axon provides more potential paths, and therefore a higher probability, for an ion to travel farther down the length of the axon before having to collide with the membrane or structures in the cytoplasm, which would slow it down. Therefore, more ions are able to move at faster speeds in a larger diameter axon, and since the speed of action potential conduction is related to the average speed of ions moving down the axon, larger diameter axons conduct action potentials faster.
The speed of action potential conduction is faster in myelinated axons because the capacitance of the membrane is reduced in the myelinated segments, which decreases the number of ions and the time needed to change the membrane potential in these areas.
In this context, capacitance refers to the number of ions that can be stored in the layers against both sides of the membrane at any given membrane potential. Unmyelinated membrane at the nodes of Ravier is thinner, so the capacitance is higher because the ions of unlike charge attract each other across the thinner membrane more strongly because of the shorter distance, allowing more ions of like charge to gather on each side of the membrane despite the fact that they repel each other. Myelination is like making the membrane much thicker, so that the capacitance is lower because the ions of unlike charge attract each other across the thicker membrane less strongly because of the longer distance, allowing fewer ions of like charge to gather on each side of the membrane since they repel each other. Because fewer ions and less time is needed to discharge (depolarize) and charge (repolarize) the lower capacitance membrane of the myelinated segments of the axon, the action potential travels faster through these segments than through the nodes of Ranvier, causing saltatory conduction.
Myelination also decreases the membrane permeability to ions, so that fewer ions cross the membrane during the action potential, and therefore need to recross the membrane after the action potential via the sodium-potassium pump. Therefore, myelination increases efficiency in terms of the energy required to maintain ion concentration gradients after action potentials. Myelinated axons have most of their voltage-gated ion channels at the nodes of Ranvier, so that while the action potential is conducted faster through the myelinated segments, it does degrade with distance, so that it is really more like a graded potential in these areas. The nodes of Ranvier, therefore, are necessary to regenerate the size of the action potential so that it can continue all the way to the end of the axon.