Washing clothes?

I think you mean Venice

The tour guides will share info on best chance to do laundry
You shouldn’t have to do laundry more than once mid trip
You certainly don’t need a different outfit for each day

There is a lot of packing info here as well

https://www.ricksteves.com/travel-tips/packing-light

https://community.ricksteves.com/travel-forum/packing

Which tour are you going on? Best of Italy starts in Venice not Vienna then goes on to the Dolomites, etc. Florence looks to be halfway into the tour which would probably be a good place to do a thorough cleaning but depending on where your hotel is. At your first group meeting, your tour guide usually gives you the best options for washing your clothes in route. A number of people, me included, bring quick dry clothes that are easily rinsed out in hotel bathrooms because I do not like to wear the same clothes over and over but that’s my quirk. I usually take some laundry sheets along. RS tour members are usually very casual in what they wear.

I will note that if you are on a RS tour, don't forget that you are responsible for taking your bag between the bus and your hotel room. Which may or may not mean stairs instead of elevators. So packing large bags may not be your most practical option. Whether we travel for a week or 7 weeks, I pack outfits that last me a week between laundries. Many items can be worn more than once before needing to be washed. And I often do a quick sink wash of delicates when staying more than one night in a hotel. Florence is a week from the start of the tour, so a sink wash, or a trip to a laundromat during your free time would work.

We have not been on a tour but since 2022, we spend several weeks a year in Europe, with a lot of time in Italy. Because our trips are for several weeks, we have to do laundry. In Rome, I found a wonderful laundress in Trastevere that I bring our laundry to and she does a marvelous job at a very reasonable price. In Florence, there is a laundromat right down the street from our hotel near the Mercato. I do a fair amount of sink laundry for undies and socks; so a lot of laundering variety. However, the one point I would make in all of this regarding laundry, specifically in Italy, in a laundromat, read the signs (unless your Italian skills are good Google Translate is your friend) because most laundromats automatically dispense the washing detergent. This can be convenient, but some of the laundromats dispense detergent with a very strong scent - just be aware.

I haven't taken the 17-day tour, but on the Venice-Florence-Rome tour, we had the option of laundry service at our Florence hotel. That was the midpoint of the trip. We were at the Hotel Silla. I don't know what your hotel will be, but as others have said, your guide will provide info.

I am sorry to hear of your wonderful pup's passing. I am glad you are finding comfort.

I am am very glad you are taking this RS tour. We took this a couple of decades past and it has been the bar that all travel since has been measured.

Once on one of our tours (not the one your taking) we did plan a laundry day. Thanks to RS we learned of a small local self-service laundry and mapped it out and planned the drop off and pick up times. We loved the experience. The laundromat was quircky and we we forntunaite the owner happend to be on site and offered to transfer the wash to dryer for us, at no charge, so that we would not have to return so soon and have more time to explore. It was wonderful experience.

That said, not every tour / stop is that congenial and I dont want to take prescious (and expensive ) vacation time to find and load a machine. Maybe you can work it out. On our 17 day BoI tour, our first RS tour, I was quite obsessed with what would become our routine. And while I am more relaxed now, it worked well.

When first arriving in a new place the usual routine was for the bus to drop us off within walking distance of the hotel perhaps mid afternoon. We'd take our lugagge to the room, immediately one of us would take out the things that needed washing and start washing and rinsing in the bathroom sink. Large pants in a small sink can be a challenge. Bring a flat oversized 'universal' sink stopper as many will not have a closer or it will leak. Wash something in the sink and toss into the shower/tub. Next item. Then rinse hem all in the tub / shower. Ring with a RS microfibre towel (gets so much more water out) and hang on a good (RS) clothes line. Bring some extra hook and loop strips to help attach the clothesline to things. We used dry sheets of laundry soap so little weight and bulk and biodegradable.

We always did this immediately on day 1 so that everything, even heavier pants were dry for packing the next night.

We did this most every stop stop maybe always just a few things and not such a big task. We'd often be last to join the group for our day 1 orientation walk but never struggled for having clean clothes. This routine woked well for us.

Sorry to hear about the loss of your pup. I know how devastating that is.

Whether travelling on a RS tour or on your own, I've found that the laundry routine is much the same. I normally try to keep my packing within a reasonable limit, with a couple of pairs of trousers, a couple of shirts and a jacket. I also pack a few pairs of quick drying travel undergarments and socks from firms like Ex Officio and others. Those can be washed in a hotel room sink at night, and they'll be dry by morning. I normally pack a small plastic bottle of liquid travel soap (usually the Tide concentrate that I use at home) in my checked luggage. If you want something to pack in your carry on, you could try the dry soap sheets. If you have a travel store in your area, they may have some products like that in stock.

For larger items, there are usually self serve laundromats in many towns. Some places also have service wash businesses, where you drop the laundry off in the morning and pick it up cleaned and pressed in the afternoon. Many of the RS tours include a free day, and that's a good time to take care of details like laundry.

I didn't notice whether this was listed in a previous reply, but if not you may find it helpful - https://www.ricksteves.com/travel-tips/health/laundry .

The RS tour guide on your tour will be able to provide information on laundry facilities.

Buon viaggio!

Also check what Doug Dymont has to say: https://www.onebag.com/travel-laundry.html#q

I’m a sink washer. I do laundry on the first night of a two night stay so it has time to dry. Here’s a few hints:
These folding hangers work good, better than RS clothes line. I take several to hang shirts and pants.
Also take a couple 2-gallon ziplock bags to wash clothes in so you don’t slosh water on the floor; many sinks are shallow or small.
I found that Forever New powder works better than soap sheets.
Be kind to the hotel and don’t drip water on the floors. I ask housekeeping for an extra towel, to blot water out of clothes.

Buon Viaggio!

I do as Horsewoofie does and do sink washing. I do recommend you run trials at home to see which of the clothing items you are considering actually do dry overnight....or at least within 24 hours.

I did this tour in 2022 when the itinerary was slightly different but as with the current tour, all stops are for 2 nights so that gives you a longer "drying time" if needed.

My procedure is to "put in a wash" when I first arrive at a hotel. I use a 2 gal ziplock as Horsewoofie mentions and then put it in the shower to soak while I go out to dinner. When I come back I squeeze out the water and hang to dry.

Each person should be responsible for washing their own clothing, lol.

As mentioned above, the guide will also discuss laundry opportunities at the opening meeting. If they don't bring it up, ask. Often there are hotels that will do it for you or there will be nearby laundromats where you can do it yourself. I think I remember that the hotels in Monterosso al Mare used to do laundry - Hotel Pasquale and Villa Steno (your group will typically be divided between the 2 small hotels owned by the same family.)

For myself, I pack light and typically take 4 short sleeve shirts and 3 pr of pants (for Italy 2 long pants, 1 capri length). This gives me 12 different combinations and....trust me on this....no one is going to notice that you are wearing the same clothing because they will be too busy seeing what Italy has to offer!

Have a great time! This tour is wonderful!

Sometimes spending a couple of hours at an international laundromat can be considered another cultural experience. I got some serious stink eye in Amboise when I removed clothes from a dryer because the owner did not return until 25 minutes after the cycle was over. Doing laundry became another travel story.

I'm a one-bag traveler these days, so I pack enough for about 6-8 days of clean clothes. I will only do laundry in the room and hang it up to dry if I'm gonna be in a place for 3 days. I will otherwise spend a couple hours in a local laundromat or....
Splurge on your $3000 trip by spending €25 to have your innkeeper do your laundry.