In Rome it is apparently never off-season, there is always a ton of tourists, as far as I've heard.
The major museums in Rome are also always busy. Vatican you need to book 3 months in advance (although very worth it), and tickets for Castle SantAngelo are apparently also always an issue (I did not go).
Tickets for the Colosseum and Palatine hill are less of a problem, you can even get them the same day if you don't mind waiting for ...probably quite a while, although the queues did not look too long. Same for the Pantheon, although the queues there are bad.
There are plenty of online resellers, but then you pay accordingly.
St. Peter's Basilica is free, and I got in with less than 1h waiting, but apparently that can be a lot worse (I was there right before the summer season started)
There is a ton of stuff to see in Rome otherwise. You don't need to reserve much time for the Spanish Steps and the Trevi fountain, but there are plenty of good museums (which I did not have time to check), like the Galleria Borghese and the Capitoline museum, or parks like the Villa Borghese or the vatican gardens.
Definitely one of the cities where there is plenty to do.
I had considered to do in the same trip also Naples (which is apparently 2h by train), and then Capri, the Amalfi coast, Pompei, Herkulaneum and the historic site of Paestum, but decided that this is worth its own trip.
Right in the surrounding of Rome there are also historic things like Ostia Antica, the etruscan tombs at Cerveteri and Tarquinia, and Hadrian's villa close by Rome (the Villa Andriana in Tivoli). So... no need to go far away.
Sicily I considered also for a separate trip, but I always want to do a lot

.