I am an AmeriCanadian living in Italy since 2009. I love Livorno as it is a very normal Italian city with lots of great places to eat and a reasonable cost of living, Living here has enabled me to see so many fantastic places in Tuscany -- you can get to everything by car or train from Livorno at the drop of a hat!
When I travel I prefer homier accommodations to hotels. and I hope that's what you'll find with this apartment. It's nothing fancy but it is welcoming, and will allow you to experience Italy in a more everyday fashion.