17 Day Best of Italy

Would you fly into Venice a couple of extra nights before the tour starts?

Yes.

Or perhaps fly into Florence then stay a few days and take the train to Venice

Depending on what flights are available, at a cost you are willing to pay, this is a viable alternative.

Rome will have the most choices for flights back to the US .

Flying from Florence probably has the least choice and may not be the most budget friendly option but should not be a killer to the planning.
How to arrange your extra days hinges on the flight availability for the various combinations. You need to plug in your dates and see what options you have

The general comments about flying FROM Venice is that most flights that head to ( connect to) the US leave very early (6-7AM) which makes for a challenge to get to the airport.

I see the order of the 17 Day trip has changed since we took that tour ( pre-covid)

We have taken 3 RS tours in Italy, although not the Best of Italy 17 day. I agree that Venice and Florence deserve more time. I would fly into Venice a few days early to get over jet lag and see a few sights not included in the tour. After the tour ends in Rome it is an easy train ride to Florence. I have found better and cheaper flights out of Rome and Milan, both an easy train trip from Florence. Have a great trip.

I also think you would enjoy flying into Venice a couple of days early. Adding a couple of nights would enable you to go to some of the other islands. When we took this tour, I wished we had more time in Venice.

Florence: I would also suggest taking the train to Florence at the end of the tour. It’s a direct route from Rome. That’s what we did at the end of our tour, but our destination was Lucca. We chose to relax in Lucca for a few days following the 17-day tour.
We then flew home from Pisa to Frankfurt or Munich (can’t remember which city) and then direct to Seattle.

If your priority is extra time in Florence, if it were me, I would book the ITA non-stop from LAX to FCO as a round trip, take the very easy train to Florence for a few days, then train on to Venice - add extra time there if you like. Then add extra time in Rome at the end if needed.

Just dealing with airports once is a luxury that it well worth it - at least to me.

I did this tour back in olden days when Venice was in the middle of the itinerary, not the beginning. I could have spent a week there. So definitely add days on front of tour for that as two nights is insufficient IMHO and getting over jet lag in a magical place like that would be my first choice. As suggested above, catch the train back to Florence at the end of the tour and then fly back home. I'd check fares for flying directly to Venice on way there, and either Milan or Rome on return (you can get train to either in under 2 hours). It looks like you can get decent connections to LAX to all of those spots.

You state you want to spend more days in Florence but are getting advice for Venice. I would fly into Milan, take the high speed train to Florence and spend the number of days you want before taking the train to Venice the morning your tour starts or a few days earlier if Venice is also of great interest. Make sure you check the tour itinerary so you aren’t duplicating interest areas. I remember we saw David as a group and had a guided tour of the Uffizi but that was preCovid. Personally, I thought Venice was extremely crowded and not that enjoyable and understand post Covid it is worse. The best part was when our tour guide took us to visit her neighborhood away from the crowds.

I have not been to Italy in a very long time but I agree with what MarkCW said about booking a round trip ticket from LAX to Rome if that's a non-stop flight for you. From there you can easily take a train to Florence and spend whatever time you want there, and then take a train to Venice, adding extra days as you wish. Then, at the end of your trip if you want a couple of more days in Rome you could add that on and then fly back home out of Rome. Of course if LAX to Milan is more convenient or cheaper you could do that on the front end and fly home from Rome on the tail end.

We are doing this tour in September, 2025 and so we are trying to figure out our itinerary also.. albeit out of Boston.