Central Europe or Northern Italty and Switzerland

Where did you go on your last trip? I ask because to me, 3 nights (really only about 2-1/2 days) would be short for Amsterdam, Budapest, Vienna and Prague. On that basis alone, I'd choose northern Italy and Switzerland. However, if your previous trip was London-Paris-Rome or something like that and you were satisfied with just 3 nights in each place, you would probably be fine with the same number of days in the major cities you propose to visit next year.

2 weeks is 12 days plus 2 to fly, so you could add one more day to one of those. I think Amsterdam would be ok with 2-fly there, take canal cruise the afternoon you arrive, Anne Frank and one art museum the next day. Remember that you must get Anne Frank tickets months in advance.

I would echo acraven's sentiments regarding the proposed itinerary for Amsterdam, Budapest, Vienna and Prague. I think they all need more time. I can speak to our itinerary in Sept. 2019. We started in Budapest, 5 nights, Vienna, 5 nights, Cesky Krumlov, 2 nights, Prague, 6 nights, Amsterdam, 4 nights. We enjoy planning day trips along the way. That said if you are limited to two weeks, Budapest, Vienna and Prague would be doable in two weeks to enjoy sightseeing, etc.

Which itinerary would offer more of what we like to do?

Naturally I pick anything that includes Budapest.

Fly Amsterdam to Prague as that opens the possibility of flying a discount airline for maybe $100 nonstop with all the upcharges or $200 on one of the big carriers. Then train Vienna to Budapest. I looked at the trains from Amsterdam to Prague and was sort of surprised at the durations. The flights from Amsterdam to Budapest are about the same on the big carriers if the discounts scare you.

sightseeing, wandering around "old towns", shopping and sampling the
local foods

That puts Budapest at the top of the list of Amsterdam, Prague, Vienna, Budapest. Cant speak to your other plan.
For that then maybe 4 nights in Budapest, then its sort of a toss up where to steal the time. Prague really speaks well to younger people, and Vienna a bit more to older; so I would steal the day out of Prague. Or leave it as you have it.

Our Central Europe transportation went like this: Flight to Budapest, train to Vienna, CK Shuttle to Cesky Krumlov and Prague. Flight to Amsterdam. Our favorite city was Budapest. We hired guides in every city except Vienna.

All those destinations have local food and shopping. Switzerlands tilts more toward the natural-beauty sort of sightseeing, as does Lake Como--though certainly the towns/cities are very pretty. The other trip would be heavily focused on urban architecture and historical sights. So it all depends on what sort of sightseeing you want to do.

Again, I ask where you traveled on your earlier trip. That would provide additional information and allow us to attempt to give better advice.

In case you are not aware, Switzerland is extremely expensive. That may not matter to you, but it would affect what places I chose to eat in that country.

Athens 2, Mykonos 3, Santorini 3 and Crete 3. We did this on our own and it was fantastic. In past years we did an escorted tour of Italy and one to France. Equally enjoyable. I know there are many tour companies that offer Budapest, Vienna, Prague with a pass through Cesky Krumlov. I'm thinking that is the way to go if we fly into Amsterdam first then start tour in Budapest.

We’ve done 6 guided tours over the years but have enjoyed more self guided trips. Central Europe is a region that lends well to self guided. Train transportation and shuttles are convenient.

Santorini and Mykonos are tiny, not at all comparable to major capitals. If you want to travel rapidly through those central European capitals, a guided tour might not be a bad idea. The tour company would take care of the hotel-to-hotel logistics and help get you oriented in each city. I prefer to travel independently, but I have lots of time (being retired) and like in-depth visits that cover secondary cities and towns.

Thank you to everyone. You have given me valuable insight for our next travel adventure.

I've made the exact trip, the Budapest to Amsterdam one. There is a lot positive to say about guided tours, but remember to do the things you want to do you will have to opt out of a lot of the planned activities to wander and munch. The nights in each place will also be up to the tour and not you. And, it will be by bus, not train. I sure prefer the train. This really is an easy one to do solo, and I suspect me, and the others here will be pleased to help. Cesky Krumlov will add a night to your tour. Nice, real nice, but not at the cost of a night someplace else. I might also reconsider Amsterdam for more time in the other cities, no flights and a stop in Cesky K.

A way to get the best of tour and self is a private guide. I just returned from Europe where I did just that, but it was a much cheaper destination.

I was told there are no direct flights from NY JFK to Budapest. It was recommended we direct fly into Amsterdam, stay two or three nights then direct to Budapest to begin tour should we take one. The one we looked at starts in Budapest.

If you want to see Amsterdam, sure. Otherwise, change planes in Amsterdam, London or Istanbul and head on to Budapest. Its all about what you want to do. You might compare the flight cost difference to lay over a few days in Amsterdam. Sometimes it adds real money to the plane tickets, sometimes not

Actually, I'd pick Italy hands down out of the choices that you give. There's great wandering among small towns and larger cities, food sampling, museums, cathedrals, views, etc.

In regards to our flights last year, we flew Seattle to Amsterdam for a short layover and then to Budapest to start our self tour. Upon ending our time in Central Europe we flew to Amsterdam for our last 4 nights. This worked best for us. It avoided an early flight out of Prague. We prefer flying in and out of Schiphol. I think either Italy or Central Europe is perfect for wandering, sightseeing, etc. All the best in whatever you choose.

First of all, all those places are great to visit.
Second, better to plan to visit places geographically closer together than waste time flying and waiting in airports.
Third, Switzerland is wonderful, but probably about 50% more expensive than Italy or Netherlands and double Hungary.

You would need more than two nights to do Amsterdam.

Budapest, Vienna and Prague would be an option for two weeks, with enough time in each to do it properly.

Budapest / Vienna / Prague is a pretty classic 7 to 9 night trip. You can buy that boxed tour from a dozen tour companies. Enough time? Depends on your style, likes and how much you enjoy them. I never would have found Budapest except for a 3 night trip. Inve been back dozens of times. I guess, knowing what I know now, I'd skip the stay in Amsterdam at a minimum, and consider spending all the in just Vienna and Budapest. But We are all different and you really can't do wrong no matter what you do. Also check Turkish Air. I prefer Istanbul's new airport over Amsterdam and my last choice would be Heathrow. But go for good connections at the best price and don't worry too much.