Italy north to south or south to north?

No reason to be concerned. The trains, roads etc., go both ways.

There is no right/wrong choice of N to S, vs S to N

Correct - the direction really doesn't matter. Something to consider though would be airline schedules - which is the most convenient aka gives you the most time. Another thing to consider is 'what do you want to do in each of these places?' Something might not be available north to south but would be if you traveled south to north. My question about the south to north though is - where are you flying into? If you fly into Naples you still have to get south to the Amalfi Coast. Where on the Riviera are you going? Is Milan the best airport to fly into, or is it better to fly out of? Hint: make the planning part of the fun otherwise it'll drive you crazy.

Weather wise, I’d rather be in the south mid September over late August, hoping the sting of summer had passed.

The prevailing winds in Italy tend to be Mistral winds, which blow from the NW to the SE. Going from south to north might mean that you will be traveling against the direction of those winds, therefore you should schedule additional time for travel with headwinds.
You will also note that when you fly back to North America, which takes longer than flying toward Europe. You can mitigate those effects by wearing an aerodynamic bike suit throughout your trip. You should be able to shave several seconds that way.

LOL Roberto.

As Robert said, makes no difference.

thanks everyone for the input. I am going to REI to get my cycling suit today. I am sure I will look good. :-)

was waiting for roberto to put his 2 cents in LOL of course you'll look fabulous ron :) happy flying

The best part of this conversation site is the great info and sometimes even greater humor! Somehow the fun we have in Italy is determined by the fun we have in planning the trip. It's even better when others join in! So: SPREAD YOUR WINGS!