Rome, Florence, Venice and Paris

I would probably fly to Paris from Rome or Pisa. It's possible to get to Paris in one day by train from parts of Italy (Milan or Turin for example) but it's a long day and may require a connection somewhere.

... My first thought is to fly from SFO to Rome but I read in past forums that flying into Venice is better......

That needs to be put in context. If flying open jaw - Rome, Venice, then coming home from Rome has the advantage of a better airport to depart from since you can get direct flights from Rome to the US. Returning to the US from Venice is not direct and generally requires a very early departure from Venice to a connecting city. Hence the recommendation to start in Venice and come home from Rome. But since you are going to Paris, that really doesn't count. Again you might have more options flying to Paris from Rome but Venice probably would work equally well. Without checking schedules I am guessing you would find a direct flight or two between Venice and Paris if you went that way. The train from Venice would be long but you could break it up with a stop in Switzerland.

Book Air France multi city from SFO to Venice, and then home from Paris to SFO.
It really matters not whether you start in Venice or Rome. The advice is often to fly out of Rome rather than Venice due to the timings of the trans Atlantic flights. This won't apply to you if you are heading on to Paris.
Three weeks allows for longer stays than you indicate...

Day 0 - Depart SFO
Air France AF83
16:00 SFO San Francisco International
11:35 (+1) CDG Paris Charles de Gaulle
Air France AF1726
12:35 CDG Paris Charles de Gaulle
14:10 VCE Venice Marco Polo

Day 1 - Arrive Venice - 4 nights
Day 5 - Train to Florence - 5 nights
Day 10 - Train to Rome - 5 nights
Day 15 - Fly to Paris - 5 nights (book this separately with any of the available cheaper carriers)

Day 20 - Depart Paris
Air France AF80
16:35 CDG Paris Charles de Gaulle
19:05 SFO San Francisco International

If you decide to fly into Venice, get a window seat on the right side of the plane (the right-hand side when you are sitting and looking towards the front of the plane) for the best view of Venice as you approach.

We are doing a very similar 3 week trip this year, in late Aug/Sept. We have 2 girls (17 & 10--going on 13!!) Anyway, I have done a lot of research and had some fantastic help from this forum. If you message me, I will be happy to share the details (number of days per location and where we are staying, costs, etc. We are flying from Seattle to Paris and back home via Rome (So, Paris, Venice, Florence, CT/Vernazza, Rome). Staying mostly in apartments- but chose a villa just outside Florence (bus every 30 min. to Florence) and a hotel in the harbor in Vernazza. Just wanted to change things up a little bit... Have fun planning!

@swan I hadn't thought to fly between Italy and France! I polled the family right after and they voted unanimously for the train.

@frank I asked the family and they like the train option to Paris stop over in Switzerland very much. Since we have plenty of time, it will be a nice way to relax and enjoy the scenery. Thank you for the idea.

@djp_syd wow! Thank you for the itinerary! That's very helpful. I'll just switch the days around to fit in a train ride to Paris

@susan I will definitely make a note of the seat choice. My daughter loves to see out the window. This will be a real treat!

@ehotchk I will message you. Can't wait to hear about your itinerary.

Ah, train to Paris. That shakes things up a bit.
In that case you are best starting in Rome, and continuing towards Paris from Venice.
You have several routes (and possible stops) to choose from if you are looking at a leisurely journey.

Through Austria & Germany ...
Venice > Verona (1nt) > Munich (2nts) > Strasbourg (1nt) > Paris

Through Switzerland ...
Venice > Milan (1nt) > Luzern (2nts) > Dijon (1nt) > Paris

So you would end up with a trip maybe something like this ...
Rome - 4 nights
Florence - 3 nights
Venice - 3 nights
Either, Verona (1nt) > Munich (2nts) > Strasbourg (1nt)
Or, Milan (1nt) > Luzern (2nts) > Dijon (1nt)
Paris - 5 nights

With your teens in mind I think Luzern and a possible trip up Pilatus would be appealing.
http://www.pilatus.ch/en/railway-cableways/

I always recommend starting in Venice rather than Rome because you're arriving jetlagged and sleep-deprived and need a day or two to adjust before being up to full speed. Venice is laid back. You can ride the vaporetto up and down the Grand Canal and watch the city slip by. You can wander the back canals and marvel at this unique place at whatever speed you want and just soak up the atmosphere. There are no major sights to comprehend, just places that are a feast for the eyes and the soul - St. Mark's, the Doge's Palace. Rome is the opposite, it's a big, bustling, noisy city, more like New York than San Francisco. And the sights are major, the Colosseum, the Forum, the Vatican Museums, St. Peter's. You will enjoy them more once you've got your "travel legs."

You should definitely stop and visit the Tuscan countryside, it's the best way to relax from busy cities such as Venice Firenze and Rome, Ceck out the Val d'orcia it's just beautiful!

David, which rail line would I use to make the trek from Italy to Paris? would I book separate trips through these cities and book my own hotel for the nights? I looked on eurail and they seem to have routes from many cites in Italy to Paris. Is this the railway you speak of?

" I looked on eurail"

Rarely a good idea. Eurail and Rail Europe do not show all trains and often mark up the tickets for trains they do show.

The easiest way to get rail schedules for almost all European trains is the Bahn (German Rail) website http://reiseauskunft.bahn.de/bin/query.exe/en, following Rick's tutorial: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules

This will only have prices for trains that start or end in Germany (so, none of the ones you will need). Once you determine how you will be breakup the trip (e.g., stopping in Switzerland), let us know your exact routes, and people can tell you which website to use to buy the tickets, and how early to book for best prices. You almost always want to buy direct from the entity operating the trains, but there are some exceptions.

If you're going to be in Switzerland a while and/or are doing some of the expensive rides like the Jungfraujoch, you may do best with a pass or discount card for the Swiss portion. For the rest of your trains, you will do MUCH better with pre-booked online tickets, as long as you can deal with no exchanges or refunds (or severe limits to these actions).

Note that the situation is different for the three countries. Domestic trains in Italy are not too expensive for last minute travel (but are still cheaper in advance), and most domestic trains in Switzerland do not have discounts for advance purchase (some do). But domestic high speed trains in France, and all trains between these three countries, have significant discounts for advance purchase, or put another way, can be exorbitant if you wait until the last minute.

The quickest journey from Venice to Paris is about 11 hours, same day, via Milan and Geneva.
So, first things first ...
1. Decide on your route.
2. Decide over how many days/nights.
3. Decide on your stopover choices.
The man in seat 61 offers some advice ...
http://www.seat61.com/Italy.htm#London%20to%20Bologna,%20Florence,%20Rome,%20Naples