If you're not considering a car hire, then you need to stay in a town that has easy connections to other parts of Tuscany. Since you arrive in Pisa, it makes sense to start from there and then move around to make it easier for your family.
If you want to include the beach, I would suggest doing Pisa first, then the beach, then heading to Florence. So maybe split up your stay - 2 nights in Pisa, 2 nights in Florence. It is easier to get to Siena from Florence if you do want to make your way there (it isn't near the coast though).
You can head to the coast from Pisa by bus - go to the beach near Tirrenia or south to north of Livorno. Take a look at this article:
http://www.discovertuscany.com/what-...n-tuscany.html
Castiglioncello is just for beach, but it is easy to reach with train. Keep in mind that it has rocky coast, not sandy beaches, right by the town.
There are special rates for train travel as a family, when you first arrive at the train station, make sure to indicate your are a family of 4 traveling and show passports to show ages. I just found a special offer that allows for kids under 15 to travel free - but you do have to buy tickets at least 2 days in advance and indicate "bimbi gratis" as the special offer -
http://www.trenitalia.com/tcom/Offer...i/Bimbi-Gratis
Depends on the itinerary. In any case, kids under 4 travel free at all times as long as they travel on your lap.
If you have to still book your hotels/B&Bs, I suggest you start from
www.tuscanyaccommodation.com and book before you arrive - this is busy tourist season in Tuscany so you'll find lots of places already won't have availability.
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