Venice and Rome apartment style hotels

I would suggest looking at VRBO for both cities. Cancellation policies vary but you can include that in your search criteria. Also, depending on schedules, early check in or at least luggage storage is possible. Worst case: store the luggage at the train stations (I'm thinking you'll be arriving by train into each city). The benefit is you can start your visit right away without carrying your luggage all around. Some VRBO apartments might let you store luggage there while the apartment is being readied for you to move in. In other words, you have options in your search. Many VRBO units have washing machines. You can include that in your search. Not too many will have clothes dryers. Payments also vary. I prefer paying by credit card (as opposed to cash upon check in). The agency will handle that, not the property owner, which gives you better options for when you pay. Hope 2022 gives you the trip you have been longing for!

As Robert notes, VRBO is a good option. I've also found apartments listed in booking.com. Those are my two main sources nowadays (that has changed a bit over the years). I have bookings thru each for an upcoming trip to Italy in March, including apartments in Milan, Venice, Florence, and Rome. I use 'advanced' searches to nail down the amenities I want (free cancellations, washer, etc) and also look at locations closely on map (consider route from train to apartment especially in Venice, e.g., one without a lot of bridges to cross while pulling suitcase). But 'free cancellation' is trickier now that it seemed pre-covid. The cut-off date for free cancellation seems to be farther out now for many places.