Anything else I should book far in advance?

Borghese Gallery in Rome. You can't get in without a reservation.

You have only 1 full day in Florence, 1 in the CT. I suggest you consider 4 nights each in Venice, Florence and Rome.

@rzolezzi
Unfortunately, I already made all the bookings, most of which are refundable. With that said, I'm not that much of an art lover, so I didn't designate as much time to Florence. I'll be back in Florence for a conference in a year, so that should allow me to revisit what I would be missing this time around.

I think 4 full days in Venice is more than necessary, but I think I'm going to fall in love with Venice.

@Laura B
Thanks. Forgot about that.

As a side note:
I booked lodging without AC in the middle of July. The hotel I booked apparently keeps some mosquito liquid thing so that the windows can be opened. Do those mosquito liquid things actually keep the mosquitos away (I attract a large amount of mosquitos)?
How hot does it get at night when sleeping? As bad as Texas?

The Domus Aurea in Rome, but it's open only during the w.e. In 2020 Nero's White House will probably become a site like all the others, if you are interested in archaeology don't miss the opportunity to visit it now.

I'd cut the cinque terre: it's nothing special, it makes you waste time to get there and the summer crowds make the all area unpleasant. Same for Pisa, if you are not interested in art...

Yes, the "mosquito liquid thing" usually works if you remember to turn it on before sunset.

I can't imagine Italy in mid-summer without a/c except for places at altitude.

Mosquitos aren't the only potential probem if you keep your window open. Italian cities tend to be very noisy. Can you say "Vespa"?