Reservations for this popular Summer of travel

For Florence, you’ve already booked what needs booking. There are also many smaller museums and other art sites that don’t need advance booking, so you can pop in as the spirit moves you, e.g., the Museo San Marco, the Bargello, Santa Croce, etc.
For Rome, you could book the Galleria Borghese, which sits within a large, beautiful park.

Chris, you don't need a reservation for the Pantheon unless visiting (without tour) on a Saturday, Sunday or holiday. In fact, I don't think that's even possible. In you DO intend to visit on any of those days, this is what you're supposed to do to make that free reservation. Go to this page of the site....

https://www.pantheonroma.com/news-events/

...and click the word "here" in the text "To visit the Pantheon on weekends and public holidays it is necessary to book the visit here at least one day in advance." The problem is that the page the click is supposed to take you too isn't coming up. I can't tell you if that's a temporary issue or because I know they're going to start charging a small fee to get in and are working out how to do that.
Whatever the case, it's MUCH too early to even think about that one so just sit tight for now.

Another excellent attraction in Rome with mandatory reservations is Galleria Borghese. Their website also appears to be down right now - an issue I've had before during hours the museum is closed - but their official ticketing website is up and running:

https://www.tosc.it/en/artist/galleria-borghese/

Forum and Palatine; not advance reservations needed but buy tickets in advance online as there's no ticket office at the site:

https://www.coopculture.it/en/poi/roman-forum-and-palatine/

Climbing the dome in Florence on a late July afternoon would probably be a pretty sweaty experience. 🥵

Happy honeymoon!!!! :O)

The Domus Aurea is worth seeing and cool underground! https://www.rome-museum.com/domus-aurea.php

It is nice in summer to rest int he afternoon, have dinner as the sun goes down (8:00 PM) then visit the fori at night. This is the link to 2022 info https://www.viaggioneifori.it/en/ but it has been the same for years so probably the same in 2023. My experience is you do not have to book terribly far in advance, but I think it would be wise to do so a few days before if you can. It truly is amazing to have an after dark experience there when it is cool. The light shows -- both of them -- are extremely well done.

We also like https://www.palazzovalentini.it/, which is indoors. Reserve well in advance for English!

I would suggest climbing the Dome rather than the Bell Tower. The views from the Dome are unobstructed and the top of the Bell Tower is like walking around in a bird cage (still impressive, though). The Dome climb also gives you up close views of the inside of the dome and much better views of the city. It is well worth the price and effort involved!

We got the Brunelleschi Pass with a timed cupola climb of the Duomo and access to 4 other sites. We did the bell tower climb an hour before. I actually liked the view from the campanile better b/c it's the only place you get an up-close view of the cupola itself. You can mush your phone up against the grid and get great shots of the cathedral w/out bars. At the top of the cupola, you see the bell tower and the city unobstructed. I might head that summer heat warning, though. It was sweaty on a 60-degree day! The Bargello, evening vespers at San Miniato (6:30pm?), and Basilica Santo Spirito were highlights of Florence not to be missed.

The Roman Forum and Colosseum were so meh without a guided tour. We did the RS Audioguide, and we had a lot of problems with the audio and map feature. Every time we wanted to stop the audio so we could get to the next spot, we couldn't get back to the map unless we shut down the app and restarted it.

Our general rule was one timed ticket/tour/big site in the morning, one free site in the afternoon (church/outside monument), open lunch, and dinner reservations made the day we came to town by our hotel concierge. It was so much fun to walk around Rome at night that we rested up at the room from 4pm-6pm, walked to an early 7/7:30 dinner, then enjoyed all of the monuments largely devoid of people until well past 10:30pm. Trevi is always busy, but other buildings aren't. Enjoy!

In Florence you might check climbing the tower of Palazzo Vecchio. I understand it isn’t as claustrophobic as the Duomo. Less tourist traffic and you still get a view of the Duomo and Campanile. We didn’t have the chance but it would have been my choice due to the claustrophobia reference.

Ah, the Borghese's official "home" site is working for me again. Here it is in case you want to do some reading about it; It also links to the same ticketing site I provided above.

https://galleriaborghese.beniculturali.it/en/

I agree that the Galleria Borghese should be considered. For me, it was one of my top experiences in Rome. Another was the Basilica of San Clemente, which also requires a reservation. The excavations are fascinating.

https://basilicasanclemente.com/eng/home-2/

Nuggets all over Rome. My faves were the Baths of Diocletian/Roman Museum, directly across the street from Termini station. Then St. Pietro di Vincoli (St. Peter In Chains), and for something completely different--hope it's still there, saw it in 2017--Villa Torlonia, a bus ride up via Nomentana from Termini. It's the wartime residence of Mussolini. Kind creepy on the March day we were there.

Villa Torlonia is still there. There are multiple buildings in the park that can be visited. It is a nice change from Roman ruins. I would imagine you can just walk up and buy tickets. I visited on a day when it was free and the weather was very nice. There were lots of visitors, but I still had no problem getting my ticket without standing in line.

Official website, Musei di Villa Torlonia