Advice for TGV travel?

I'm traveling to Europe. Flying into Paris, staying for 3 days, taking the TGV
to Avignon, staying for 3 days, then wanting to travel by train to Siena or
Florence (staying for 3 days) then flying out of Pisa.

I can't seem to get a route on the Eur-rail TGV from Avignon or Nice to Siena.
Their website doesn't seem to want to make that connection. Can anyone tell me
if it is possible to take the train like that? Please excuse my ignorance.
Any information would be helpful.
In addition, can anyone recommend a place to stay in Siena or Florence that
would accomodate a family of 4 for around 150 Euros a night? (Or less)

Thanks so much.

--Mary