Cinque Terre / Portovenere in late November

Late November is not a great time to go to the Cinque Terre.

I would play it by ear when you are in Florence. If the weather is bad (rainy or cold or both), just stay in Florence and skip the Cinque Terre. Leave if for a better time in a future trip.

If the weather is not bad, I would skip it anyhow, but if you want you can go, however consider that most establishments are closed, the hiking trails are closed and it's not beach weather.

If one has to absolutely go just to say you've been there, then I would go just for the day from Florence (2.5 to 3 hrs each way). Depart early because the sun sets early that time of the year and there is nothing to do at the CT at night in winter.

If you absolutely must spend one night (2 nights at the end of November would be pure masochism) then Monterosso is the obvious choice. It's the biggest of the 5 villages, with more chances of finding hotels that aren't closed for the low season. Also more trains stop in Monterosso than all the other towns.

Portovenere is not part of the Cinque Terre and is not connected by rail (you need a bus from/to La Spezia, then walk a few blocks to the station), therefore you shouldn't consider it at all. The Cinque Terre villages are (in increasing order of distance coming from Florence): Riomaggiore, Manarola, Corniglia, Vernazza, Monterosso.

I was in CT in early October 2013, and wanted to visit Portovenere for a day, ideally by boat. While the sea seemed pretty calm to me, the boats were not traveling in the morning. Maybe in the afternoon for the return trip, I was told, if the sea is calmer. So I made the trip in the morning, train to La Spezia, walk several blocks to find the bus stop, wait for the bus, then 30 minute bus ride to Portovenere. The town is quite similar to the CT towns, probably a little less quaint and scenic, think I. The trip to and through La Spezia was certainly nothing special. In the end the boats did not go out in the afternoon either, and I had to repeat the same process to return to the CT by land in the late afternoon. Dubious that the boats would be out in late November, and doing the day trip by land in either direction is not worth the time and effort, in my opinion. I doubt that Portovenere would be any more active than the CT towns in late November, but others may have more knowledge about that than I do.

In Italy in November, I'd try to get your small-town experience concurrent with a truffle festival, such as at San Miniato in Tuscany or Gubbio and others.