beach recommendations in Livorno
Ciao K4te,
It sounds like you're going to have a great mini adventure in just four days in Tuscany. I like your itinerary, it will cover a good amount in such a short time
I'll comment on the Livorno and beach part - the coast is really clear and nice in that area, just know that the beaches are mostly pebblely (not sure that's a real word LOL! ). Mostly smooth stones, but be prepared, not sandy.... sandy is further north toward the Versilia or further south around Piombino and then on in Maremma. It still a great area to enjoy the coast and sun!
So as for beaches.....
There is basically one rocky beach in Livorno you can actually walk to (or take the bus) just south of the
Naval Academy:
http://www.comune.livorno.it/portaleturismo/index.php?page=_layout_spiagge&id=56&lang=it
The rest are heading south, little by little, along the coast and are near Livorno.... you can get to all of these with bus #1 from Piazza Duomo or along Via Grande in the direction of "Miramare" so you won't have a problem moving around without a car. The bus basically runs parallel to the coast, so you can get off, explore, continue along the line.
Here's the schedule for the summer:
http://www.atl.livorno.it/Orario Estivo/feriale/Urbano Livorno feriale.pdf
the first pages are already for bus #1.
Here are some of the beaches:
La Rotonda - in Ardenza
http://www.comune.livorno.it/portaleturismo/index.php?page=_layout_spiagge&id=57&lang=it
Scoglio della Ballerina - in Antignano
http://www.comune.livorno.it/portaleturismo/index.php?page=_layout_spiagge&id=49&lang=it
Cabianca - in Antignano
http://www.comune.livorno.it/portaleturismo/index.php?page=_layout_spiagge&id=58&lang=it
To all of these beaches, the bus ride is 25 minutes or less.... so they aren't far at all.
Castiglioncello is also a very nice town, but a bit further south than Livorno - you can get there by train and then walk a few blocks to the rocky beach. I remember you need water shoes in this area as you do end walking over a lot of rocks to get in and out of the water.
Have you already booked accommodation? Recommend you use
www.tuscanyaccommodation.com to get started, gives you a good idea of what is available. When we were in Livorno last fall, we actually stayed at
Hotel Gennarino which is right in front of the Naval Academy and really liked it. It was walking distance to the Terrazza Mascagni and a bit further from downtown, but we walked there too! All the houses in the area are in this Liberty style with "medieval" tower elements, it was pretty neat

.
Hope these suggestions are useful -- hope you have lots of fun!!

Feel free to post any other questions!