What to do with luggage

My experience is that yes, hotels do, but not the vacation rentals. You can Google each location for the availability of private luggage storage or train station lockers.
Safe travels.

Hi there -
Just curious? Is this the order of your itinerary?

Venice, Florence, Rome, and Sorrento (2 nights each except 3 in Rome)

I know it wasn't your question but if Sorrento is on the end, I hope you don't need to be in Rome the next morning/midday for a flight out? Hit a transport snag and you're too far away for (my) comfort. Sorrento can also be a time-consuming place to get to so could eat up a chunk of the partial day you'll have there.

2 nights = only 1 full sightseeing day.

If your hotel won't do it, try Stasher. I used Stasher in London and it worked out well. They contract with local businesses who will hang on to your stuff while you're out and about.

Venice, Florence and Rome all have left luggage facilities in the rr stations.

Some vacation rentals will hold luggage, some rail stations will, bit there are also small businesses that will hold luggage foe a fee. Apps/websites like Nanny Bags will list businesses near you that will take luggage. I learned about the pub across from the Salisbury train station who took luggage, even at 9a.m. I think I got that from TripAdvisor forum.

I have used https://radicalstorage.com/ on this vacation and was satisfied. I have the app on my phone so it is easy-peasy.

I guess it and stasher mentioned above are basically the same. Maybe even using the same agents.

Another company to check: https://usebounce.com/