Proposed Florence Itinerary…any help or comments appreciated!!

I wouldn’t do a 3 hour class on arrival evening

Be sure to visit inside Basilica of Santa Croce

I would group San Lorenzo street market with Mercato Centale, Medici chapel rather than all that back and forth

Siena deserves a full day
Bus from Siena to SG is convulted and time consuming so if you must visit SG it’s best to do a guided bus tour although that won’t allow a lot of time in any of those locations

You could easily combine Lucca and Pisa on a DIY day trip

Where does the Chianti wine tour start?

I liked Siena better than San Gimignano. The Piccolomini library in Siena is beautiful. I would spend more time in Siena and skip SG. I have not been to Pisa as I have no desire to see the tower, but I might go there to see the Cathedral some day. I am a big fan of Museo San Marco in Florence, more so than the Medici chapels.

I wouldn’t do a 3 hour class on arrival evening

I'd agree. Besides being too tired to pay attention, most of us don't advice booking anything for arrival day due to potential flight delays or cancellations. Most tours/classes are non-refundable if canceled day of.

Siena deserves a full day

I'd agree with this too. Set aside a full day.

Be sure to visit inside Basilica of Santa Croce

Definitely.

Duomo (make rez)

The duomo is free. As far as I know, you can't make reservations for this one. They do offer a guided tours but not on Saturdays.

Duomo Dome climb 463 steps narrow?? Make rez

To climb the dome you'll want to purchase the Brunelleschi Pass. You are required to make a timed-entry reservation for the dome at time of purchase. With this pass you don't need to make reservations for the bell tower. The time you choose for the dome starts the validity of the pass as applied to the other included structures (the climb has to be the first thing you do before visiting any of the rest). Climb the dome AND the bell tower same day? That's pretty ambitious, IMHO.

https://tickets.duomo.firenze.it/en/store#/en/buy?skugroup_id=3006

Your May 22nd itinerary is too full, IMHO. Palazzo Pitti is a collection of 5 museums - around 140 or so rooms - under one roof. It is very large and takes considerable time to see, even if you don't do ALL of the museums. The Boboli Gardens also cover a vast amount of ground. I know we spent over 1/2 a day there, and that was without doing all of the museums and most of the gardens. It's a real time-and-shoe leather gobbler. Still I'd recommend it over spending much time with the shops on (overcrowded) Ponte Vecchio. I loved that bridge but think its best face is anywhere but ON the thing!

Piazzle Michelangelo
Yes it's a must. I'd love to see you make time for San Miniato al Monte which sits even higher than the piazza. It's a very, very old and important church.

May 26 Monday Visit Lucca in morning and have lunch there Chianti
Sunset Safari Tour with dinner at 4 pm

IMHO, this is pretty ambitious too and doesn't leave much time for Lucca.

I am a big fan of Museo San Marco in Florence, more so than the Medici
chapels.

I'll agree with that too.

Thank you all so much for all this great advice! I have implemented everything you suggest!

Depending on what you decide to do with the Duomo sights, if you have time, I'd highly recommend popping into the museum. It's just next door and is included in all of the passes. I think it's incredibly underrated. It's recently renovated so it's very comfortable, air conditioned, bright, and well maintained. No crowds! Not a huge time commitment, but they have very impressive reconstructions, original doors, famous artworks, etc. It was definitely one of our favorite sights last year in the city.