Help with 3 1/2 week travel itinerary!

24 nights means a maximum of 9 destinations from how I see your needs and style of travel.

07/12 Arrive Zurich. Then to Luzern (2N)
07/14 Train to Lauterbrunnen, Swiss Alps (3N)
07/17 Train to Lake Como (2N)
07/19 Train to Venice (3N)
07/22 Train to Florence (2N)
07/24 Fly Vueling Airlines VY6364 from Florence to Santorini (3N)
07/27 Fly/ferry to Athens (3N)
07/30 Fly Aegean Airlines A3658 from Athens to Naples. Then to Sorrento (3N)
08/02 Train to Rome (3N)
08/05 Depart Rome

Aligunter,
You have a good plan, even though you are visiting a lot of places. I think your Switzerland travel is fine. Note, Switzerland is very expensive, plan on spending from 50 to 100 percent more there than in other places surrounding Switzerland.

Southern France nice, but the rivera is also expensive. Southern France is best done with a rental car, not sure you want to do that. St. Paul de Venice in France is wonderful, as many places on the Rhone River. Florence deserves more days.

Greece is wonderful, especially the islands. Athens has many great ancient sites, but has gone downhill recently, due to the economic problems of the country. You might consider skipping Greece, saving the airfare and spending more time in Italy. You can visit Capri, the Amalfi Coast, Pompeii, etc.. also spend more time in Florence and Rome. Rome is awesome.

Thank you for your input, David and geovagiffith! I hadn't considered the flight to Greece coming and going to separate cities so that might be wise to maximize time and travel. Good to know about how much more expensive Switzerland is, especially since we will be on a show string budget. I would be happy spending our entire time in Italy, but I know I'll never convince my kids of that so I'll throw some of these ideas around for them. Keep em coming!

Wht is a reasonable amount of money to budget for daily expenses (not including lodging)? Is it possible to purchase groceries rather than eat out every meal?

Thanks again!

I haven't been to Switzerland in several years.

Here is what I found on the internet
https://www.numbeo.com/cost-of-living/country_result.jsp?country=Switzerland
Meal for 2 People, Mid-range Restaurant, Three-course 100.00 Fr. The Swiss Franc is now pretty much on par with the USD.

According to this, a meal for four at a nice, but not luxury restaurant would be $200. A meal at McDonalds would run $14
Meal, Inexpensive Restaurant 20.00 Fr.

Venice would be more expensive than Florence or Rome, but your cost in Italy would likely be about 2/3 of the Swiss estimate.

You can find less touristy places to eat and save. Rick Steves and Frommer's Guides could help you there.
If you stay at B&Bs your breakfast would be included.

Grocery stores would be a savings, especially if you found an apartment to rent with cooking facilities. Airbub may help you there.
https://www.airbnb.com/?af=2404406&c=A_TC%3Da8n4hcekq2%26G_MT%3Db%26G_CR%3D13806338379%26G_N%3Do%26G_K%3D%2Brent%20%2Bvacation%20%2Bapartment%26G_D%3Dc&dclid=CJO8472_sNECFZARhgodkLkORw

Grocery stores are not always easy to find in the central parts of European cities. You are more likely to find small stores like you find in NYC.

If you have more questions, I will be glad to assist.
George

That you fear the teenagers may be too ambitious is a good sign; surely that means they're excited about the trip, right?

There have been several threads in the last 2 or 3 months that addressed the issue of how to eat inexpensively in Switzerland. Browse the Switzerland forum and you should get some useful info. You can certainly create some picnic meals from supermarket food, for one thing, but on the forum you'll find some additional suggestions.

The usual recommendation for seeing the Swiss Alps is the area around Lauterbrunnen. Murren seems to be the top recommendation for the base city. If, as I assume, you want to do some walks up in the mountains, be aware that the weather is unpredictable, so you should plan several days in the area in hopes that at least one is conducive to getting up high,

Check prices of the high-alpine transportation that goes to or near the mountain tops before committing. Those things are extremely expensive if you don't have any sort of Swiss pass, and the passes pay off better if your in the country for more than a few days.

Personally, I wouldn't go to Greece (and deal with two flights in the middle of my vacation) for just a few days. The country is more than Athens/Santorini/Mykonos. But if it's one of the top 2 destinations for several people, I realize it may be hard to say "No". Athens is all about the Acropolis and the museums. The Plaka excepted, it's a pretty modern city. I wouldn't allocate a lot of time to Athens. Hotels in Santorini can be very expensive.

Getting to and around the Amalfi Coast takes some time, so that's something you might take a look at fairly early on. Once you've allocated sufficient time to Venice-Florence-Rome and Switzerland, you may find that you don't really have time for both the Amalfi area and Greece.

As far as a schedule, David is second to none. But you may want to factor in some rest days with nothing to do but rest. You may need them after 5 to 7 days. With a 10 year old and an infant, I found that every five days works for us, but we are up with the sun. Another tip is that the average tourist sleeps late while on vacation in Europe so to the most famous attractions are less crowded early. In addition to hotels, you may want to consider staying at a few hostels. It will give them a chance to interact with some others who are traveling.

Thanks csu.
Fortunately, ali's destinations (Swiss Alps, Venice, Santorini, Amalfic Coast) all lend themselves easily to some relaxation time.

Thank you everyone. I'm making progress. Natures House is closed for renovations summer 2017 so we booked 3 nights at the youth hostel in Grindlewald. I think we will cut out the Amalfi Coast. I really wanted to see it, but it sounds like we'd need a car and I'd prefer to avoid the crowds and extra expense. So I am trying to decide if this is a good plan:
Grindlewald 3 nights
Greece 1 week
Florence 4 days
Venice 3 days
Rome 1 week

Am I missing something obvious that would easily fit in? Spending too long in Greece or Rome? Open to your suggestions!

Actually, my son really wants to see Italy by train so I'm rethinking flying from Switzerland to Greece and following a schedule more along the lines of the one David provided (thank you!). I've read a lot of people suggest 2 nights for Venice is plenty, but see you've allotted longer there than Florence. I'd love to hear why...isbit just personal preference?

Neither here nor there with Florence vs Venice.
It depends on if you have plans for many day trips from Florence and how many museum/churches you intend to visit.
With Venice, in many respects, it is just in being there and soaking up the atmosphere.

Got it.
Im trying to decide whether to break up a week between Rome and Sorento, or stay the whole week in Rome and plan some day trips. Opinions?