lots to do!
Ciao Dave and welcome to our forum!
When are you coming to Italy? Your planned itinerary sounds really good so far, particularly breaking up and inserting Cinque Terre after Florence.... train from Venice to reach Cinque Terre if you wanted to do it right away would make you pass through Florence anyways, so it makes sense to do Florence in between!
I ask about when you're coming because while this is the Meditteranean, the water for swimming along the Tuscan coast tends to be cold up until June (I am from California, I like it nice and warm

LOL).
So for this reason I am proposing heading "inland" for your itinerary rather than staying along the coast... you could do this:
- after Florence, head west to Pisa, Lucca or Viareggio. See and experience the coast of the Versilia, then off to the Cinque Terre.
- after Cinque Terre, pass through Pisa on the way back toward Siena. I recommend it as a good base from which to see both Chianti and the area nearby because it has good connections (mostly by bus) to the surrounding area... not great, but there are many tours you can also join in from there. From Siena you can visit San Gimignano, Volterra, Monteriggioni, some areas of Chianti such as Castellina, all by bus.
You can catch some ideas for accommodation in Siena here:
http://www.tuscanyaccommodation.com/siena-city/
... without a car, it will be hard to stay in the countryside, the same for visiting places. A good way to get around that is to do organized tours. Have no direct experience with these - mytours.it - but they offer several tours out of Siena that would be interesting.
The whole area to any side of Siena is wine country - you'll eat very well in Siena as well but if you head north, you have Chianti, to the south the Brunello di Montalcino and Rosso di Montepulciano, to the west San Gimignano the white wine called Vernaccia, to the east Chianti from the Arezzo hills... if you do tours, they'll take you to ones they're affiliated with, generally smaller estates that you would never ever hear about outside of Italy.
As far as hot springs go, there are many all over Tuscany - including several towns that grow around the springs - if you looked at a map, all of the towns with "terme" in their name have springs, such as Montecatini Terme, San Giuliano Terme near Pisa, Chianciao Terme near Montepulciano. Most of these hot springs have been taken inside buildings, very nice spa places and only a few remain that exist outdoors, such as the ones in Saturnia, some at Bagno Vignoni, some outside of San Filippo terme. All of these really require you have a car to reach.... so maybe you can look into renting a car once you leave Cinque Terre?? Rather than doing tours, you could rent a car and go around on your own.... it might make it easier for you to do a mix of things and to stay in the countryside - see some of the places you could stay at here:
http://www.tuscanyaccommodation.com/siena-farmhouses/
Just to entice you
