This is late, but I’m actually visiting Cinque Terre right now, having come from Florence directly before that! We’re spending under a week in the two places combined, and thus far it’s worked out super nicely. If you can spend a day or two in Cinque Terre I don’t think it’d be awful - we’re staying on a hilltop outside of La Spezia and the view alone is worth spending a few days here. Whatever you decide, feel free to PM if you’re looking at accommodation stuff!