Prague or Cesky Krumlov

To avoid backtracking do C.K. on your way to Vienna. Are you aware of open jaw? You are flying to Milan then the same day to Prague. From NYC there is a direct nonstop flight on Delta to Prague. So I would fly from NYC to Prague and then from Milan to NYC and save a lot of time and maybe money too.

You don't have time for all of these transfers. First - although Cesky Krumlov is a cute little town, it's not worth the effort on this already-rushed trip. I agree with the previous poster about going straight to Prague if you haven't bought your air tickets yet.

Budapest to Rome is way too far to transit by bus or train on this itinerary. That would take you an entire day and then you'd just have to leave to go to Milan. You should save Rome for another trip.

What makes the most sense is just Prague, Vienna and Budapest. If, for some reason, you already have a ticket and MUST fly home from Milan, you'd likely need to fly from Budapest to Milan - it's about 1200 km.

If you already have air into and out of Milan and you haven't been to Italy, what about spending your time there? You'll do a lot less transiting.

In a 10-day trip, you should not be visiting Rome or Cesky Krumlov for one day. You don't explain if you have found low-cost airlines to make these big jumps. But you will spend so much time with airport transfers that you should go directly to Milan and see something irreplaceable like The Last Supper - which you will not have time to do if you are only there for a night (not "a day" , but for "a night"). Book The Last Supper immediately.

I mean, at least Venice is on the way to Milan. Why are you going to Rome for 12 hours?

why are you flying into Milan when you are not spending any time there, makes no sense to me whatsoever.

Whenever I fly into Europe, it's open jaw--into one city and out of another. And I don't fly into and out of another 3rd party city because backtracking is (1) expensive and (2) time consuming. Remember every time you move from city to city costs you a whole day. And your arrival and departure days are wasted getting from and to the airport.
If you've not paid for your flight, I suggest changing it. Of the 3 cities, Vienna is the only one with flights directly to JFK/Newark and that's on Austrian Airlines.
Limit your trip to Prague/Vienna/Budapest as they're all about 3 hrs. apart via train.

And if at all possible, grab an extra day or two for the trip.

First off thank you for your responses, appreciate the help

I fly in and out of Milan, because I was fortunate enough to receive a compensated plane ticket from a flight I took to Milan last year for my Italy trip.

I'll look into what open jaw is, I never heard of this before.

From Budapest to Rome, I would fly. It's a 1.5 hr flight. When I went to Milan, Iast year it wasn't my favorite, I was there for a few days , I was lucky enough to see the Last Supper, I didn't enjoy the food quite as much. I wanted to either go back to Venice or Rome, since I didn't see a direct flight to Venice, so Rome won. The next day my plan is to take a train from Rome to Milan to make my flight home.

Hope this makes me sound less crazy haha. It's my in betweens of Prague to Budapest I'm seeking advice for in regards to bus and trains. I apologize for not being clearer.

I like Cesky K. but because of the time you have I suggest

Day 1 - Flight from NY to Milan
Day 2- Land in Milan, fly to Prague
Day 3 - Prague
Day 4 - Prague
Day 5 - mid day train Prague to Vienna
Day 6 - Vienna
Day 7- Vienna
Day 8- Morning train to Budapest
Day 9 - Budapest
Day 10 - Budapest
Day 11 - Budapest to Milan

Wizz Air flies direct Budapest to Milan for $88 or to Bologna for $102 according to Google Flights. If you need to spend a night in order to make a connection then:

Day 1 - Flight from NY to Milan
Day 2- Land in Milan, fly to Prague
Day 3 - Prague
Day 4 - Prague, evening train to Vienna
Day 5 - Vienna
Day 6 - Vienna
Day 7- Morning train to Budapest
Day 8- Budapest
Day 9 - Budapest
Day 10 - Budapest to lay over city
Day 11 - lay over city home

My opinion, of the three Budapest requires the most time, then Prague and then Vienna. But depends on your tastes.

In order to not miss your flight home, you should plan to be in Milan the night before your departure back to New York. Since you'll be on separate tickets, it's too risky to plan a connection that morning (and it may not even be possible, depending on where you're coming from).

Open jaw flights are found by looking for "multi city" or "multiple destinations" on airline booking websites.

Thanks everyone, I really do appreciate the advice.
We've decided to drop Cesky Krumlov from the plan and stick with the three main cities.
Unfortunately, we did book a flight from Budapest to Rome and purchased train tickets from Rome to Milan, crossing my fingers everything will work out in the end.

If the Budapest - Milan direct flight fits your schedule I sure would consider it for an additional $88 Your train tickets from Rome will cost that much.