Florence itineraries fail when they try to do Uffizi, David, and the dome in one day. One ticketed interior per morning.
2 nights: dome and Uffizi
Day one: Duomo climb and Oltrarno dinner. Day two: Uffizi, Ponte Vecchio, Piazzale Michelangelo. Train in from Rome; train out to Venice the next afternoon if you are on the classic 10-day route.
3 nights: add David or Chianti
Keep the two-night core, then Accademia or a Chianti afternoon — not both if you dislike rush. This is the comfortable Renaissance chapter.
With Rome and Venice
Rome 1.5 hours south, Venice about 2 hours north. Book both trains with the gallery tickets, not the night before.