How to see both south of Florence (Siena) and North (up to Lucca) over a 6 day period

HI and thank you in advance for any help you can give us on planning our trip!  My husband and another couple will be landing in Florence on November 28th around 1:00 in the afternoon (coming from the US) and here is what we are thinking…..would love your insight and any input all of us enjoy wine, food, enjoy walking through and around towns, seeing some historical sights (not big museum/cathedral touring though), some shopping in local areas and enjoying the culture with more locals than tourists Originally we were thinking we would make our base in Lucca, traveling to Pisa, Cinque Terre, Montecatini while also having time to just sit, enjoy a coffee and soak up Tuscany
However, then we started looking at Siena and wondering if we should make that our base, traveling to Chianti, San Gimignano and the Val d Orcia area….
NOW, were wondering if we could split our time between the two and see all of it
We will be headed to Naples on December 4th via train at some point in the day (leaving from Florence seems to be the best idea but feel free to give input here too and spending 5 days in Naples (mostly working but some sight seeing as well) then to Sicily for 4 days (mostly working but some sight seeing) and flying home from Naples on December 15th. So we want to see different sights in Tuscany than we would in those two areas (which is why we weren’t going to visit the coast much in Tuscany)….
We were told the Rapid bus from Florence to Siena is great transportation….and that the train from Pisa to Florence is direct, only takes approx. 50 minutes and we could get from Lucca to Pisa easily on a train the day we need to head back to Florence. Other than that we don’t have any set ideas of transportation other than we don’t want to get car sick
Thank you sooo much for your help. At this point we don’t even have accommodations figured out between hotel or apartment/villa…
Look forward to hearing from you,  Luke and Casey