Dina, the tall and short of it is that weather is going to be a crapshoot: it could be sunny and reasonably warm, and it could be chilly, windy and very wet. It could also be somewhere in between. The problem with the CT is that when the weather is lousy, there's no a lot to do. The villages are very small, and some of the businesses/restaurants may already be closed for the season.
You're also allowing very little time for the CT and Rome. By the time you subtract your transport time, you're left with 1.5 days of sightseeing for each. Honestly, given just 4 nights, I would have flown directly to Rome and stayed there for the duration: you'll barely scratch the surface in 3.5 days. That one also offers more indoor attractions to see when the weather doesn't cooperate.
One other reason for spending all of your time there is that the 6th is a first Sunday of the month: all of the National Museums are free and mobbed on that day, and the Vatican museums are closed. It's not as if there won't be some other things to do but it would leave you only the 7th cram in the biggies (Colosseum, Vatican, etc.) if some of those are on your to-do list.
That said, if you keep your plan for the CT I would suggest Monterosso as it's the largest, has the most accommodations, and will likely have the most still open in early November. I'll have others suggest hotels as we loved the location and view from ours but it's a no-go if you want a large room. It may also already be fully booked at this late date.
If it were me, I'd save the coast for another time and go to Florence, if you want to do 2 locations. You can get to Rome from there in 90 minutes by the fastest direct trains. We loved Firenze: lots to do and see, wonderful Medieval architecture and glorious Renaissance art.
One option: should the 5th be dry and sunny, you could day-trip to the CT from Florence. There is a 7:38 AM train leaving from Firenze Campo Di Marte station at 7:38 that'll have you at La Spezia Centrale by 9:11. You're only a few minutes from Riomaggiore (and a few more minutes to others of the villages) by local train from there. It returns from La Spezia at 19:59, arriving at Firenze Campo Di Marte at 21:40. These is the fastest way to do it and involves no changes between Florence and La Spezia.