Hi Sandy,
Here's a list of some of the festivals in Italy.
https://www.ricksteves.com/europe/italy/festivals
Also, here's the 2020 schedule for the Roman arena in Verona. I attended an opera there (wonderful!), but there's other events, too.
https://www.google.com/search?source=hp&ei=smSZXavACtHG-gSRq4LADQ&q=verona+opera+schedule&oq=verona+opera&gs_l=psy-ab.1.2.0l10.1007.3885..7861...0.0..0.184.1202.6j6......0....1..gws-wiz.......0i131.WWMOxVzWorQ
There's so many options for festivals. I went to the Arezzo Jousting Festival two years ago, and I've been to the MITO (Milan/Torino music festival), Stresa Music Festival, and Venice Regatta. I would recommend looking up each town you're considering on-line with "festival" or "activity" and see if they have anything scheduled.
Since you're planning to go to Pisa, you might want to consider stopping or staying in Lucca. It has an intact medieval wall that's the perimeter of the old center. The wall is wide enough that it's a popular spot to take a stroll, ride bikes or enjoy seeing the locals socializing at the benches.
Outdoor food market - several towns have these. Check your towns for day-of-week of Outdoor Markets
Stay at a B&B in a vineyard or Agritourismo - numerous in Tuscany. Check booking.com or similar sites
Walk past a quaint apartment buildings with a lot of flowers on the balcony - not sure about your apartment reference, but overflowing flowers from balconies are all over the Dolomite region
Outdoor restaurant/ Family owned restaurant - I only eat in outdoor restaurants in Italy when the weather is nice. Family owned ones are all over, if you walk a few blocks away from the tourist hot spots.
Grocery stores - I stop in grocery stores at almost all towns I've stayed in (20 towns). Don't touch the produce; use a plastic glove. Just watch the regular shoppers do it, first. Also, it's good to bring a bag for your groceries.
Locals hanging out on benches in the city center - again, this will be easy to see
Children playing outside right there on the cobblestone streets - Venice comes to mind immediately. In areas away from the Rialto bridge to San Marco route.
Maybe a celebration of some sort going on - ideas listed above for you.