Help with physical challenges

Jo, most large museums have elevators. If you don't see a sign for one, ask. The word is "ascensore". Train stations with elevators will show the symbol of a person inside a box on the info sign for tickets, toilets, etc. There may be escalators as well. Almost every museum has benches so you can take a break if necessary. Enjoy Italy!

For Venice, the challenge is the many bridges with stairs; you'll need frequent rests, and while the non-stair parts of town are flat, there are almost no places to sit. I don't know if you'll find it difficult to get on and off the vaporetti. Be aware that while the line 1 along the Grand Canal uses larger boats, many of the other routes use smaller boats with much tighter spaces and less seating (as I recall, I often had to go downstairs to get a seat, or even standing space). Florence will be easiest; it's flat in the center. In his book, Rick has information on minibuses that go through the center (larger buses skirt the center). For Rome, the subway (whether there are elevators or not) only goes to some useful places. Buses are the mainstay of transit there, and they are often very crowded (you can NEVER expect a seat). So, you should plan on taking taxis for any long distance, any time you feel tired, and any time you anticipate a lot of tiring activity (for instance, you should take a taxi to a museum, so you aren't worn out before you get there). To get a taxi, you don't hail them; you go to a taxi rank, or call for one (if you call, the meter starts when the driver gets the call). Many museums have loaner wheelchairs. The one time I did this, in Dresden when my mother had sprained her knee, we had to leave a passport as "deposit"; I don't know if this is common. I can say the wheelchair made the visit much better; don't hesitate to use one in a museum, even if you don't need one the rest of the time (as you say, the museum walk is much harder than regular walking).

Jo, some elderly friends of mine just returned from time in Italy, and they found the collapsable canes that have a little seat to be very helpful. You'll find elevators in most major museums including the Uffizi, you just have to look or ask. They are often out of the way. Also check the website vatican.va in the Vatican Museums section; I believe they have a page describing services for the handicapped. One of the challenges might be finding hotels with elevators. I often use convents, which almost always have elevators (for elderly community members). The high end hotels will also have them. If you want budget hotels, you may just need some research; some in Rome and Florence have elevators; Venice may be a little more challenging. And ask for specifics... sometimes there's an elevator, but you have to climb a flight of stairs to get to the lobby/elevator or to get from the top of the elevator to your room. For Venice, try to determine how many bridges you'll need to cross to get to your hotel. They are commonly stepped inclines and could be tiring, particularly with luggage. If you can minimize the number of bridges, the walking is flat and usually well paved. In other cities, I'd suggest you budget for some taxis to save energy. The Rome metro can have lots of stairs, sometimes with elevators/escalators out of order. For trains, the best thing you can probably do is pack very light. Even in good condition, it can be challenging to get on trains and get luggage stowed away. Most train stations do have elevators, tiny ones, at a far end of the platform. When I traveled with my mother, I remember having to keep expectations under control, budgeting time for resting with a coffee or gelato in pleasant settings for people watching. Enjoy!

"sometimes there's an elevator, but you have to climb a flight of stairs to get to the lobby/elevator or to get from the top of the elevator to your room." This point is worth emphasizing. I've lost count of how many times I've had to climb stairs (sometimes just a few, but at least once a whole flight) to get to the elevator in a hotel. On a related note, it's common that even though a restaurant will be on ground level, the bathrooms will be up or down a flight of stairs (often steep). I don't particularly remember this in the cities you're visiting (it's more common in Paris), but do be wary.

Jo, you picked possibly the best weather, so that's good. I learned during July this year to have the courage to ask if where the bathroom is before I decide to 'rent' a table for a rest and bagno use. The shopping malls all have them. Downtown Naples was okay for me this year, but its port geography means a steep decline from, say the Teatro San Carlo to the waterfront castles. There were posts on the streets which you could grab if you decided to do the challenge. If you park at a garage (better for the slow traveler), it's a few blocks to the main shopping/attractions. If you ask for help, or have to sit on a bench and join strangers, everyone was splendid. Taxis can take you from point to point. Who cares if it's 3 blocks? Lastly, the farmacie are wonderful for pain killers. Come to think of it, so are the wineries! In 2012, I did not have the courage to quit. That was a big mistake. I love my people watching experiences as much as anything else!
You'll have a wonderful time.

Good point about pharmacies, which can dispense heavy-dose painkillers without a prescription.

Due to an injury related weak ankle I use a collapsible cane when traveling. Very useful when negotiating cobblestone sidewalks, ruins, and stairs. On the buses in Rome I was frequently offered a seat, and also on the metro. To get into the colosseum it is necessary to climb quite steep and crowded stairs with high steps - there is an elevator that will take you to the higher levels - just make sure members of your party know where the elevator is so they can meet you....