April 2022

April isn't exactly beach season in that part of Italy. And with only 10 days, you don't have time for it if you also want to see the big 3. If you give us some idea of your itinerary, we might be able to provide some suggestions.
Have you read any of Ricks Italy guidebooks or watched any of his videos?

Check out the "itinerary" here -- https://www.ricksteves.com/tours/italy/venice-florence-rome

As you are doing r/t from Rome, trying to hit all three is essentially impossible. You would not have the dedicated bus for door to door service and you have to back track.

Pick 2.

Edit- It appears the OP has made a revision to how much time they have. Original comment above was predicated on '10 days total'. If it is '10 nights' then the suggestion by jmauldinuu ( further down) works. And valadelphia makes a valid point that seeing Venice-Florence-Rome is not 'mandatory'.

I agree with Joe. I like Venice a lot; it is special. But better to have an enjoyable trip to Rome, Florence and some other spots in Tuscany than subject yourselves to a Rome-Florence-Venice-Rome death march.

Do you actually have 10 nights on the ground in Italy, or does that include the overnight plane trip to Rome?

Is that 10 days on the ground or does that include your travel days (8 nights)? When I had two weeks vacation I could usually squeeze in 6-7 more days by using the weekends and also try to get a paid holiday in there for one more day. If you have not yet booked your flights you should consider flying into Venice and home from Rome spending 3 nights in two places and 4 in one (I would choose Rome).

If your flights are already set, and if you actually have 10 nights on the ground, you could see all three cities this way: Land in Rome in the morning, immediately take a train to Venice later that morning. You will arrive Venice in mid afternoon; that first day is already a jetlagged day so might as well use to to travel to your furthest destination. Then spend 3 nights in Venice, 3 nights in Florence, and 4 nights in Rome. This way you are already in Rome on your day of return departure. During one of your days in Florence, take a day trip with WalksofItaly or ToursbyRoberto. Both are highly recommended on this forum and both will give you a lovely day excursion into Tuscan villages, vineyards, etc. Some of their day tours are more focused on wine than others, so read the tour descriptions. Look at train schedules on trenitalia.com. I prefer to take late afternoon or evening trains when changing from city to city, and eat my dinner on the train. This gives me the most daylight hours on the ground sightseeing.

You do not necessarily have to see the "big three" of Rome-Florence-Venice on your first trip. Rome and part of Tuscany or even just sticking to Lazio (the region of Rome) would be a perfectly acceptable choice! There are some interesting Etruscan sites in Lazio and southern Tuscany that are close to the coast if you wanted a peek. I love history, but I tend to prefer outdoor sites like ruins/tombs, etc. over spending long days in museums, and Italy truly has it all.
April can still be a tad chilly, so I would not necessarily make the seaside a priority, but you should plan the trip you want. Trying to do too much the only mistake.
You can enjoy good food and wine virtually everywhere, so I suggest getting a detailed Tuscany guide book and dig in until something strikes you. Do you have a favorite wine or something that might spur suggestions?
I only get ten days for a typical vacation, and time can seem to slow down magically if you plan well!

Leave the beach views for the next trip and see Venice then plus the Cinque Terre. This time round make it Tuscany and Rome leaving Rome for the end of your stay.
If your flight arrives in Rome late morning take a direct train from the airport to Florence’s SM Novella station (2h 30m); otherwise, you’ll need to transfer.
Day 1 – sleep in Florence.
Day 2 – sleep in Florence.
Day 3 – take a morning bus to Siena (1h 15m) and sleep there.
Day 4 – take a direct bus from Siena to San Gimignano (1h 15m) for the day, sleep in Siena.
Day 5 - take a direct train from Siena to Montepulciano (1h 15m) and sleep in Montepulciano.
Day 6 – take a taxi from Montepulciano to Pienza and explore the old town; sleep in Montepulciano.
Day 7 – take a train from Montepulciano to the Chiusi-Chianciano station and transfer to Rome’s Termini station. Sleep in Rome’s Trastevere neighborhood. If you’re unable to find a place in Trastevere, try the nearby Hotel Smeraldo located across the River Tiber.