Italy in February!

Great places, even in the Winter. Still, it will be late Winter and warming up.

You are avoiding the Easter season so crowds in Rome will be less that during Easter.

I love using TripAdvisor.com checking "things to do in -----"

Rome is my favorite city with the ancient stuff as well as St. Peter's Basilica and the Sistine Chapel.
Florence has two wonderful art museum, Academia and the Uffizi.
Just walking around and taking in all the amazing architecture in Florence is super. Of course, don't miss going into the Doumo, Bapistry and Tower. There are day tours that visit other key historic sites.
Venice, do a gondola cruise (negotiate with the boatman), do St. Mark's Basicila and the Tower at the square. Also, tour Doges Palace and walk over the Rialto Bridge.

Congrats, Sarah!

We've been to Italy twice in exactly that timeframe, and it's wonderful. Just prepare for occasional cold & rain, you never know...

First, if you can work it to fly into Venice & out of Rome, you'll be a step ahead. Trenitalia Venice/Florence & Florence/Rome, book ahead. From there the canvas is blank. Because you won't be driving, stay at highly-rated hotels in central areas so you can walk everywhere, or if you've been to Italy before, try an AirBnB.

These are the 3 most visited tourist areas, so anything 'with locals' might be manufactured. But...a cooking class is always fun--those are locals that cater to tourists. But to live with locals...you'd probably have to stay in a small town. Also, it being (every quarter century) Jubilee 2025 year long, I'd make advance reservations for anything--including restaurants--that for sure you want to visit.

Do research online & see what appeals to you. Come at us with specific questions and we'll try to help you out.

Enjoy your planning!

Each city has a page here on the RS site. They are a good place to see what's available and what appeals to you. Check the AT A GLANCE section.
https://www.ricksteves.com/europe/italy/florence

Congratulations!
If you don’t already have it get a copy of RS Italy guide book-it’s chock full of great info, logistics etc
You will need to prebook all entries to major sites-San Marco, Uffizi, Accademia, Colosseum, Vatican, Borghese, etc so do some research here on time frames for obtaining those tickets and be ready when they come available -some may already be-not sure anymore but the info can be found here
When you search the forum be sure to filter by Type and Date

I assume you will travel by train-you can buy those tickets now if you are sure of dates
Use the official Trenitalia website or their easy to use app

https://www.trenitalia.com/content/tcom/en.html

We did the three cities in mid March 2023, loved all of it! A couple of things to share:

I found Italo trains to be a little cheaper, especially their no refund (or restricted refund) advanced booking trains. But, probably best not to use that on your arrival days, just pay full price if you are taking a train the day you arrive.

We started in Florence, spent 6 night there. We bought the Firenze card and used the extra days (5 days total) but we wanted to concentrate on museums the whole time. That might not be the way you want to plan your time, so you might want to consider just prebooking Uffizi and Academia. You can also purchase one of the combined tickets for the Duomo, depending on whether you want to climb the dome and/or the bell tower. I was very impressed with the duomo museum which is part of all of the combined tickets. Florence is a very compact, walkable city.

We did Venice 2nd and by then were slightly museumed out so we spent most of our 3 days just wandering on foot, taking the vaporetto when we got tired. We bought a 3 day transit pass which was well worth it, we saved a few $ purchasing online before arrival then retrieved it at a machine near the train station. We did go to St. Mark's cathedral - went one day without a ticket, line was long so just used our phone to book a ticket for a few hours later. We also went to Murano, it was nice, but we picked a foggy day and only needed a few hours to be ready to head back. In Venice consider booking a free reservation to visit the roof top at T Fondaco Tei Tedeschi - it's a high end department store with a roof top terrace, they allow people to go up for 15 minutes just to look around and take pictures. there are no services up there, it's just a view point, but it's free and a fun thing to do. Unfortunately they are ending it sometime this year, but I think it will still be available in March. You can only book a few weeks ahead.
https://www.dfs.com/en/venice/service/rooftop-terrace

In Rome, we did a food walking tour of Testaccio neighborhood (Eating Europe was the tour group). It was fantastic! It lasted about 4 hours, on a Monday, we had SO MUCH food. This was the first time we ever did that type of tour, have since done it in a few other cities, but this one is still the best!

We used Rick Steves free audio walking tours, especially in Florence and Rome. We each had our own headphones and the tours loaded on our phones and we just tried to stay at about the same timing for the tour. the tours provide you an introduction to neighborhoods or museums that might be overwhelming otherwise. You can download them and listen before you travel to see what you think of them.

I believe someone reported on this forum that the Fondaco dei Tedeschi viewing terrace in Venice is closing soon because the shopping center shuttering. It won't hurt to check, though. I wouldn't count on being able to get an online entry appointment for San Marco after you arrive in Venice, though I suppose it's possible you'll be able to do that in the Feb-Mar timeframe. It would be better to take care of that ahead of time so you know you won't have to stand outdoors in Venice in the winter, when the weather might be rather raw. You should be able to get tickets for most of the other sights in Venice on the spot in the winter. The Secret Itineraries Tour at the Doge's Palace is popular on this forum, and it does sell out in advance at least part of the year. I don't know what the situation is like in the winter. Individual vaporetto tickets are a painfully expensive at 9.50 euros per ride, so the advice to get a suitable multi-day pass is excellent unless you are confident you will move around almost entirely on foot. Here are the prices for the passes:

24 hours: 25 euros
48 hours: 35 euros
72 hours: 45 euros
168 hours (7 days): 65 euros.

Even with a pass, you must tap the validator before boarding the vaporetto for each ride.

If you want to see the Sistine Chapel in Rome, you need tickets to the Vatican Museums. Those are likely to sell out ahead of time. The Vatican sells plain-vanilla entry tickets (and you can rent an audio guide if you like, or listen to Rick's guide for free), or you can book a tour conducted by the Vatican or by a commercial tour company. The Vatican's tours are cheaper. Some tour companies offer combination tours of the Vatican Museums plus St. Peter's Basilica. The advantage of those is that the tour groups usually are allowed to use a connecting door between the Sistine Chapel and the Basilica. Without that provision, visitors who want to see both buildings must walk some distance from the Sistine Chapel back to the exit of the Museums, walk outdoors around the outside of the building, and stand in what is likely to be a very, very long security line at the Basilica. The Museums and the Basilica will probably be a bit less busy in Feb/Mar than later in the year, but I was in Rome during Mar 2023, and the sections of the Museums along the most direct path to the Sistine Chapel were unpleasantly crowded. And 2025 is a Holy Year, expected to send more visitors to Italy and especially to Rome.

You can buy Vatican Museum tickets here: https://tickets.museivaticani.va/home/fromtag/2/1740373200000/Biglietti-Musei. It appears the Vatican's tours aren't yet on sale for your dates; they should be available on that same website if you want a tour and are comfortable waiting to make the purchase.

There is no entry fee for St. Peter's so there's no way to buy a ticket ahead of time to circumvent the long security line--unless you take a commercial combination tour, as mentioned above (which will probably cost in excess of 100 euros per person).

Online tickets for the Colosseum usually sell out earlier than tickets for the Vatican Museums; I don't know how early that will happen in Feb/Mar. They changed the ticketing procedures about 11 months ago, to try to keep tour companies from grabbing so many of the tickets. Still, if you want to see the Colosseum, you should check immediately for information here on sales procedures. It would be prudent to buy Colosseum tickets the day they go on sale for your desired date, and it's possible you'll need to get up in the middle of the night to grab them as they are put on sale. (But only if you feel you have to go inside the Colosseum; the exterior is free to view.)

Another sight in Rome for which tickets should be purchased ahead of time by those interested in seeing it is the Borghese Gallery.

Forgot to mention the weather situation.

I didn't go north of Rome during my Feb/Mar 2023 trip. I was lucky in that I believe the high temperature every day at least hit the monthly average. One definitely cannot complain when it plays out that way. However, for most of my trip it didn't really get up to 40F until around noon, and it cooled down from the daily high temperature quite quickly after the sun went down (which happens pretty early at that time of year). Be sure you have appropriate layers you can put on and take off and put back on during the day. If you don't want to tie said layers around your waist (which I acknowledge isn't a stylish look), you might like to have a day pack or a lightweight tote bag to hold the garments you aren't currently wearing.

You might encounter high water in Venice. I don't know how likely that is. I was glad to have waterproof shoes in Venice back in September, but most people seem to manage without them. They put up elevated walkways along the heavily-traveled paths, but I couldn't get out the door of my hotel without walking through a large puddle.