Lucca, Livorno or Siena?

Siena would be my choice

You could combine Lucca and Pisa

Ditto for me.
Siena: first choice
Lucca+Pisa: second choice.

Siena. The Siena Duomo and Piazza del Campo are as good as it gets.

I've day tripped to Pisa and Siena from Florence and have visited Lucca for the day while on the road on a RS tour. Easy train ride to Pisa and subsequent walk (of course you can taxi if prefer) to the tower and Field of Miracles. Comfortable bus ride to Siena (use Express version to get there faster) during off-season was easy-peasy. All destinations are terrific in their own right and it really depends on what you most want to see / visit. I'd do a little Google map research and walk around each locale to get a sense of where things are and what the pedestrian distances are. Time of year will have an impact, if during high season April to October you'll want to be judicious on early start and having a plan on activities you want to experience for any location visited. Loved biking the ramparts in Lucca, had an incredible guided tour in Siena with the incomparable Anna Piperato and while not climbing the tower had a wonderful self-guided time in Pisa, including a tasty lunch. I say no wrong answer among those three. Which one interests YOU the most?

Siena … more Renaissance.

Lucca and Pisa … more Late Medieval. LATE NOTE of course, Galileo was Late Renaissance.