What time do you arrive in Rome? What time do you depart from Venice?
What time does friend arrive in Venice and from where? what time does she depart?
A 3 night stay equals 2.5 days, a 2 night stay equals 1.5 days, etc
Having friend meet you in Florence is a great idea- if she wants to experience both Florence and Venice. It’s not much further on train than Bologna and easy enough to do. She takes airport bus to Venezia Mestre station and then purchases tix on next fast train to Florence (or can use the app once en route from airport). Look up train possibilities ahead of time, they are frequent and direct (no changes)
You and friend #1 would then spend 3 or 4 days in Rome before heading to Florence for 3 or 4 days.
Make a list of what you want to see/do in both Rome and Florence then decide which location gets 4 nights. (2 with other friend)
If you want to do a day trip from Florence (Siena, Lucca/Pisa?) then then you should give Florence 4 nights and day trip should probably be on Monday or other friend would not really have much time in Florence (depends what time she arrives but I have to assume it would be mid to late afternoon)
Then you all take train to Venice on Thurs 12/4
You and friend #1 get Rome 3, Florence 4, Venice 3 (or 4-3-3)
Friend #2 gets Florence 2, Venice 2
That’s a pretty standard first 10 day trip to Italy- covers the Big 3.
Would look like this:
Thurs 11/27 Arrive Rome- jet lag day
Fri 11/28 Rome
Sat 11/29 Rome
Sun 11/30 Florence or Rome
Mon 12/1 Florence (museums closed- good day for day trip)
Tuesday 12/2 Florence- friend arrives Venice- takes train to Florence
Wed Florence 12/3
Thurs Venice 12/4
Fri Venice 12/5
Sat Venice 12/6- friend departs
(while there are great day trips from Venice I wouldn't since now you only have 2.5 days in Venice)
If you don’t have a good guide book- get one. RS Best of Italy works. You can get it quickly on Amazon.
Meanwhile you can start here:
https://www.ricksteves.com/europe/italy
Check the At a Glance for each location you are interested in.
Trenitalia- the official train company- fast trains and regional trains
https://www.trenitalia.com/en.html
Use Italia Station names
Roma Termini
Firenze SM Novella
Venezia S Lucia
(Venezia Mestre)
ItaloTreno- private fast trains only
https://www.italotreno.com/en
Both have easy to use apps.
You can book your tickets to Florence and Venice once you have itinerary set and save some money but you don’t have to book in advance- there are multiple trains all day long.
There are hundreds of threads here about all things Rome, Florence and Venice-use the Search function (filter by Type and Date) for anything- lodging, sights/tickets/tours, how to get around, eats, etc
Post any questions here- you will get tons of help.
If Friend #2 decides to met you in Florence we can give specific directions for how to do that.
Be sure you all figure out how you will get to the airport for departure- it’s a bit involved from Venice. Lots of threads on that topic here as well.
If you book any venues in advance (most big ones will need) make sure you are using the official sites- ask here for those links as you need them.
There are some spammy websites out there now that must be avoided!