58 yo woman solo sabbatical Europe- Help me please!

If you can go any time after March, I’d choose April for less crowds and cooler temperatures and fly into the most southern city first and out of the most northern city. The three places you mention for your 4 week trip would probably require intraeuropean flights to connect. It might be good to know what your interests are to organize your itinerary.

You must book or settle the airline ticket first today.
What city do you fly out of?
Book it into Rome and out of Lisbon.
You could fly into Rome from the USA and tour Italy
Then train to Paris then fly to Lisbon.
Then fly home from Lisbon.
Once you settle the flight first, then fill in the blanks

From our experiences-
Avoid the week before and the week after Easter. Also avoid the May 1 Labor Day holiday in Italy, along with the weekend after. Always check out the big holidays in any country, and try to avoid them, because of crowds and closures.
Have a wonderful adventure!

Generalizations dont work for me. Probably best to book your tickets by the end of the year. The week prior to Easter might be an issue some places, here in Budapest its full of street vendors and celebrations. Easter Sunday? Go to church and experience the culture.

March or April? Maybe warmer in April, maybe wetter in April. Possibly a lot wetter in May.

My choice for you? A complete random selection based on absolutely no input: Paris, Budapest, Rome, Lisbon. Four flats a week each + or - and lots of day trips. Discount flights (cheap) between each.

Well as another 58 year old woman I would suggest looking at a couple of different options. Personally I could easily do the entire 4 weeks in Italy, or in France, so that might be a consideration. If I really wanted to see more than one country, I'd pick two. I love both Portugal and Italy, but think that Italy just has a bit more to see. ( One trip I've wanted to do is start in Paris and finish in Rome, taking trains between them all). Three countries will mean a lot more transport logistics and to me would take away the enjoyment.
I like April travel as well, it is a bit less busy and temperatures are manageable .

If you are going to be by yourself for this, I personally would stay in a hotel with a breakfast. And a smaller hotel would be ideal. You can chat to the owners or who checks you in and get advice on where to go, how to get there etc. And it feels a little less lonely potentially. You could also consider monastery stays in Italy.

The other thing to suggest is that if you are moving around a lot, make sure your luggage isn't too heavy. It always feels mysteriously more heavy when you land with jet lag!

Lisa makes a lot of good points.
Despite my love of Portugal, 3 different countries in 4 weeks may be a bit much. But if you decide to include Lisbon I would be glad to add my suggestions. April of May would be good months, Warmer yet before the crowds descend.

Where are you departing from? If one of the three cities have a direct flight for you, that would influence my itinerary.
If staying at a hotel, check for laundry options.
Don't buy your tickets until about 3 months before you leave

I will follow this post and jump in if I have anything I think is helpful

Enjoy

I think the answer depends mostly on you. Are you a city person? If not, a week each in four big cities might get overwhelming by the end. Are you up for switches in culture? Then try four countries in major cities for a monthlong sampler trip. Are you a planner or a go-with-the-flow traveler? If a planner, consider that four countries will be more work than 2 countries.

For the actual “where”, with this opportunity, I say pick where your heart says - not what we say. You will get a lot of different opinions, but ultimately it is your trip and if you pick where you want to go, then it will be a good trip.

You have plenty of time, so first think about what your interests are. Then see how to get between those places. For example, train from London to Paris, but fly Paris to Budapest (just examples). Sometimes budget flights don’t go every day. Once you know those things, you can start looking for places to stay. Remember it’s ok to move more often than once a week if you want. For example, you might want 4 nights in Rome and 3 nights in Florence. Or maybe only 5 nights in Paris before you move on. But remember 2 nights equals only 1 full day, plus longer transitions really does mean most of a day in transit. With a month, there’s no need to rush.

Hotels are easier than apartments, but they are sometimes more expensive and you usually have less room. Why not pick a combination? Pick places close to public transportation (a bus or tram or metro stop). I use both booking.com and air bnb - what I find depends on where I am going. Filter for what is important to you: private bathroom, breakfast, free cancellation, air conditioning, etc.

Buy multi-city plane tickets: for example fly to Paris but home from Lisbon. Look at prices of different combinations - like into Rome and home from Paris, etc.

What an exciting time! You will find a lot of us here are kind of obsessive about planning! I love the planning part nearly as much as the going part. Ha!

A couple of thoughts:
1. re: Itinerary planning. Make a list of places you'd like to go and things you'd like to see and do in those places. I use a spreadsheet for this and add links to sights and restaurants. This document will be the basis for your itinerary for this trip, as well as your bucket list for future travel. Throw it all in at the beginning so you know how long you need in each place. At this point, put it in order of priority, not in any geographic order. Be open to possibility because...
2. re: Transatlantic flights: Think about what is "best" for you, which might be a direct flight, short flight duration, low airfare, using accumulated miles, comfort, etc. Then start figuring out what is available to you that fits that bill. For example, after Covid, I had a LOT of Alaska miles, and they had a good deal for business class tickets on Condor, SEA-FRA. Two ticks for that (comfort and paid for with miles), but I wanted to go to Ireland. Easy. Three nights in the glorious Mosel Valley, then fly FRA-DUB. Google Flights, Skyscanner and sites like The Points Guy or Nerd Wallet for maximizing points programs. Flightsfrom.com will show direct flights from your home airport. Remember that you can buy open-jaw tickets or separate one-ways.
3. re: Friends: Have a serious conversation with the friends who are serious about joining you. Find out when they are available and where they want to go (and why). Figure out if they are going to rely on you to plan this part of the trip or if they will take the wheel (if this makes a difference to you). If you have a friend you know you can travel with who is 100% in for a week in Paris but can only go the third week in April, well you decide, but I would calendar that and work around it. Friends have to be all in or all out, no waffling.
4. re: When to go: Ideally, the first day you can, but definitely April or May. I wouldn't wait until September or October because you might be ready to go again by then. To me, summer is right out for Paris (and just about anywhere in Italy or Portugal, too). Too hot, too crowded, just no.
5. re: Where to stay: I am a default AirBnB person, but I stay in hotels or aparthotels, too, depending on where I am, who I'm with, etc. Once you know your destinations and your companions, you can come back to the Forum to get lodging recommendations.
6. re: Putting it all together: Flights between European cities are generally quite inexpensive (again, SkyScanner or Google Flights), but trains are part of the experience, IMO. The best source of information is The Man in Seat 61 (seat61.com). Be warned, the site can be a bit of a rabbit hole.
You can do this. Just be thoughtful and organized, and it will come together.

OK, I have a different suggestion.....since you're not sure where to go, where to stay, etc....

How about starting with a Rick Steves tour of Italy? A tour will help you see more and not have to worry about transit between towns and hotels for a few nights.

Heart of Italy starts in Rome and I would be there several days ahead of time. These tours start back up in mid-March but there are a number of dates thru April.

https://www.ricksteves.com/tours/italy/heart-italy#tour-dates

The Best of Venice, Florence and Rome tour would be great too and just be one night longer than Heart of Italy.

So...something like this:

Days 1/2/3 - Fly to Rome. Overnight Rome. This gives you 2 full days before a tour start to get on local time and see a few things.

Days 4 -11 Heart of Italy tour which does Rome, Volterra (small hill town), Cinque Terre (beach location), Florence

Days 12/13 - Florence (because like Rome, 2 nights/1 full day is not enough for Florence!)

Days 14/15/16/17 - Take the train to Venice and spend 4 nights in Venice

Day 18 -24 - Fly to Paris. Overnight 7 nights in Paris. There are several airlines including some of the Low Cost Carriers like EasyJet that fly the route from Venice to Paris.

Day 25 - Fly to Portugal for your ending week there.

Just a suggestion for some structure to your trip.