You can either go Rome--Florence--Venice or Venice--Florence--Rome (pick whichever gets you the best airfare). Take trains between the cities. (Though 8 days is a pretty quick trip that won't give you much time in any city.) You could easily spend 8 days in any of these (and I have). I'd say 2 nights Venice, 3 nights Florence, 3 nights Rome, but if you prefer Venice, spend 3 nights there and two in Florence (the trip between Florence and Rome is the shortest). Given how short a time you have, I'd spend extra to book central hotels. This is just a start, and there are people on these boards that know Italy much better than I do so I'm sure you'll get better and more detailed advice from them on the other issues.

I believe Delta and United are the only airlines that flies nonstop from New York (JFK & EWR, respectively) to Venice, and they both fly from Rome back to NY. The flights to Venice might be seasonal only so you'd have to check the airline schedules.

You could also fly into Rome and out of Venice. It's a belief by some that flights to the US leave Venice at o-dark thirty, but that's not the case for flights to NY. The United flight to Newark leaves around 11am which gives you plenty of time to get to the airport by either boat, or bus if the weather prevents the boats from running.

8 days, while a pretty quick trip, would give you at least a few days in each city, eg 2/3/3 like Doug suggests, or 3/2/3 since your day of arrival is basically a wasted day. Of course you could spend far more in each city, but that would give you a flavor.

Definitely use trains between cities. Others (eg Pal) will weigh in with more info about trains and the price advantages of booking ahead.

You don't say whether the eight days includes travel time. Flights from NY are generally overnight, so if that's included in the eight days, that only leaves you seven nights. Really not enough for three cities. If you insist on all three, another possibility would be to take a day trip to Florence from Rome. Or, leave Venice early, store your luggage at the Florence train station, have some time in Florence and then continue on to Rome.

I agree that with so little time, stay in a central location. In Rome, the Piazza Navona is a good location. Near a lot, plenty of restaurants, good bus connections.

Before you commit to visiting all three of these wonderful cities in the same short trip, make sure you've considered the advantages and disadvantages of doing so. You can see a bit of each, but you certainly can not see even all the highlighs in the little time you would have in each, and you would spend a chunk of your time in transit, rather than exploring those cities. And as already noted, you'll lose at least a part of your first day to jet lag.

For train information, consult seat61.com

If you are OK with this being a familiarization rather than immersion trip you'll be fine. October should be a lovely time weather-wise. I'd start in Rome (3 or 4 days) then train to Florence (2 or 3 days) then on to Venice (1 or 2 days) and home from there. I expect to get bashed by Venice aficionados, but I find it a place everyone should see once then leave with overpriced trinkets and fond memories.

For our upcoming trip we are flying nonstop both ways on United from EWR, arriving into Rome at 0745, leaving from VCE at 1105 am.
If you sleep well on planes you would have almost a full day in Rome on arrival. Keep in mind as you plan that most museums in Italy close on Mondays - except the Vatican, which closes on Sundays - if that matters to you. Agree with Doug that centrally located hotels are a good idea to minimize time spent in transit.

Trains are operated by Trenitalia or italo with italo usually a bit lower on fares, especially with advance purchase. Transit Rome to Florence is just under 90 min on fast trains; Florence to Venice is just over 2 hours on fast trains. Unlike on longer journeys, on such short trips I find the "cheap seats" fine and the "perks" of first class not all that enticing unless you can get a great deal on the fare.

I think 3 major cities in only 8 days is trying to see and do too much. I loved Venice and so many people cut it short.

I would pick only 2 cities for me that would be Florence and Venice. But for you I would look at flights and see what is the most convenient to fly in to and out of. And yes then move around between them by train.

Or just do all 8 days in Rome

That can mean seeing a very tiny bit of 3 places or seeing a bit more of 2 places or seeing a fair amount of 1 place. To my way of thinking, every moment of transportation can be interesting, but is time spent NOT seeing "as much as you can." Just something to consider.

With that info I stand by my original recommendation. The perfect (endless time and money in every place) can easily be made into the enemy of the good (8 days, 3 venues) but through a lens of realism if you have this time and these desires, go for it. It is not a moral failing to skip/have to miss some aspects of a place. For example, the chance to spend a day in Venice is better than never having seen the place. And who knows, you may be so enamored of one stop that you make it a priority to visit again.

For some people, that is definitely true! For me, I'd rather skip something entirely than skim it, and because the world is so full of places I want to see, I am reasonably sure that I will never return to any place I have visited, however briefly. No right or wrong answers here, just pros and cons to each option.

As others have said, with only 8 days you'll just get a taste of each city - but that can be a wonderful thing. I've spent far longer in all those places but a couple years ago I did an 8 day trip to those three cities (plus was flying in and out of Milan so that took time you won't need to). I did the trip with a friend who had never been to Italy and we both (her the first timer, and me who had been multiple times) had a great time.

Here's the trip report I did - Italy thru new eyes / Chasing the sun in March

If you click on that report there's also a link to the blog which includes photos.

I was able to add one additional day to the trip but can't do more than that. If anyone has recommendations on hotels, locations, restaurants, please let me know. Also any "under the radar', more local must sees would be appreciated. I booked my airfare so now going to spend more time researching itineraries, etc. Thank you all!

https://www.lacalcina.com/
Well it's one very small tidbit but I LOVED this hotel in Venice. I've stayed there twice. As far as must sees, I just wandered around with no specific itinerary when I was solo. With a friend he had some printed out self-guided walking-tours that we did that gave some structure to our city walk abouts. Definitely take the #1 vaporetto that runs on the Grand Canal.