Car Rental vs. Train in Western Italy

First of all you are trying to see too many places in such a short time. Every time you leave a location and travel to a new one you need to plan on 1 day to check out, travel and check in. I always prefer to take the train when in Italy as the drivers tend to view road laws as suggestions. And, I agree, parking in many places is difficult. I would decide which of these places are easiest to get to via train and cut my list to 3 areas, e.g., Florence, Rome and the Amalfi coast. In your itierary you are flying in to Milan, then renting a car and driving to Genoa. I never recommend driving after just getting off a long flight. In this case, I would fly into Milan, stay one night, then head to Cinque Terre. And, is there a reason for visiting Genoa? It is a pretty industrial area. You could take the train from Milan and cut out Genoa all together. I use the website Rome2Rio alot when planning my trips as it gives transportation options with times between cities.

Any advice is appreciated. Are you sure? 'cause most is not going to be good. It is simply -- you rent a car to go where public transit cannot take you in a reasonable amount of time. All of your stops are major cities/area that are well served by trains. AND -- you really need to rethink your schedule -- For example - if going to Rome, put it at the end of your schedule. Way too much driving and one or two too many stops. You really need to get a map and put some pins in to get a feel, geography, where you are going. Not the the best plan --- IMO.

I agree--too much traveling and not enough being there, plus driving jetlagged and quite likely sleep-deprived is dangerous to you and all the others on the road.

For your last night you need to be in or very near Rome. Things could go disastrously wrong if you wake up in Positano and try to get to Fiumicino Airport (over 180 miles away) three hours before your flight (I'm assuming it's back to the US or Canada). Positano has no rail service.

If you miss that flight you'll be paying the walk-up fare for two one-way tickets, which will not be pleasant. My policy is to be within an affordable taxi ride of my departure airport the night before my flight, just in case of a problem with the public transportation I plan to take. I once planned a visit to the Amalfi Coast and found there was a general transportation strike on the day I was traveling. No trains or public buses were running.

Make sure all the wedding expenses are refundable, because after going on the trip you have planned, you will probably be a bachelor for the foreseeable future...

All kidding aside, your plan is not a good one - for all the reasons pointed out above:
1. Do not fly to the other side f the world, arrive exhausted, jump in a car, and drive away to a tragic accident. It's really dangerous and not worth the risk.
2. Genoa? Not a great choice, given all the other places you could spend that time and how short your trip is.
3. Forget Genoa, forget the car. Everywhere you are thinking about going is best served by trains. A car on a trip like this would only be an expensive, hassle-filled headache.
4. You do not have enough time for all the places on your list. How many full, usable days do you really have in Italy (not counting your arrival or departure days) - looks like maybe 10? With that many days, pick 3, maybe 4 locations maximum.
5. On such a short trip, you need to limit both the number of times you pick up and move yourself (change locations) and the geographic extremes you are trying to include. Settting aside Genoa (which does not seem like a smart choice to include, unless you have some very special reason to go there - ie meeting family), you have two "outliers": Cinque Terre in the north, and Positano/Naples in the far south. You don't have time to get to/from both, so pick one or the other, not both (both are "seacoast" places, both will be crowded, both would be insane to drive to). Personally, I'd skip CT and just to Positano, but that means longer distance to traverse).

Among all the options of things you could do after flight arrival, sitting on a train is one of the easiest (other than sleeping). There are a few afternoon trains that run directly from Milano Centrale station to Monterosso, usually around 12:00, 14:00, and 16:00, which take 3 hours. Assuming your flight arrives a couple of hours earlier than those times, you could get all the way to Cinque Terre on the first day. Or, you can get to Florence even faster - frequent high-speed trains take only 1h40min. It does not much matter which you choose first, since either Florence or Cinque Terre have fine connections southbound.

Cinque Terre 3 Nights
Florence 3 Nights
Positano 3 Nights
Rome 3 Nights

Much better schedule. But one thing I will guarantee is that if you are sitting on a train after an overnight flight, you will be asleep. The train will rock you to sleep. So make absolutely you know your schedule arrival time for your end destination and set an alarm in your cell phone for about 30 minutes prior to that so that you are awake and prepared to get off. Been there, done that.

Thanks for all of the advice so far. The primary reason I was thinking Genoa is it seems like a good "driveable" distance from Milan, and would allow for a short visit in the Ligurian region on our way to Cinque Terre. Check into Cinque Terre, spend a day and that night, then head to Florence for 3 nights... Good advice on the last day. Maybe go from Florence to Positano, and then to Rome. I can add another couple of days to the trip as well. Based on the feedback so far, I'm thinking that is probably in order.

I do kind of like Laura's recommendation of:

Cinque Terre 3 Nights
Florence 3 Nights
Positano 3 Nights
Rome 3 Nights

My follow on questions are:
1. Are all reachable by train?
2. If we want to do day trips in any of those areas, what is the best means of transportation accomplish that?

Thanks again!

The longer the better - always!

Agreed,
If I go the following route:
Cinque Terre 3 Nights
Florence 3 Nights
Positano 3 Nights
Rome 3 Nights

Are all reachable by train, and If we want to do day trips, what is the best means of transportation to accomplish that?

Yes, all are reachable by train. You can safely assume anywhere in Italy except a small village is reachable by train.
Cinque Terre is, as the name suggests, an area containing 5 towns (Monterosso al Mare, Vernazza, Corniglia, Manarola, and Riomaggiore). Each has a station, so when you get down to detailed planning you will need to decide which town you are staying in.

Follow Laura's plan, it is a good one.

I could say a lot more, but I suggest you read this web page, which will tell you all you need to know about Italian trains: https://www.seat61.com/Italy-trains.htm

There's inconsistent information being provided above. I'm virtually certain there are no trains to Positano. There is bus service. Some people arrange a private driver from a relatively nearby spot that does have rail service (Sorrento? Naples?). Obviously, that's a somewhat costly option.

I did a search on this, and the answer I found was: Train to Salerno; Then ferry to Positano.

Or train to Naples and then train to Sorrento and then bus to Positano; or train to Naples and then ferry to Sorrento and then bus to Positano; or bus to Positano directly from Naples; or ferry to Positano from Naples.

Positano isn't reachable by train, but it's definitely reachable by public transport.