Everyone’s preferences are going to be different, but here are a couple of ideas. I am going to give 16 days as two weeks with all connected weekends is 16 days. Don’t forget that once you get to Europe the low-cost carriers can get you from point A to point B for under $50 in a lot of situations. That makes the world pretty small. You can go to Google Flights and type in a starting city and use “Europe” as the destination, then narrow it down by Non Stop and under $100 and your options become apparent. The only useful airline that doesn’t show up for some reason is Czech Air so you have to do that search the old way.
Besides no dates or time of year you didn’t discuss budget much. Tell met the budget is $300 a day and I have all sorts of ideas beyond these two.
1 NYC to Kyiv. Sure, why not. Be adventurous
2 Arrive Kyiv. This place is just plain fascinating. If it clicks with you, you will be back, cause a day and a half isn’t enough.
3 Kyiv
4 Kyiv to Lviv non stop on Ukraine Air for about $50. Lviv I think will be the Krakow of the future. Thanks to Ryanair, starting this fall, you can fly direct on to Budapest. If you are going before the fall, then move on to the next idea I have (but your loss)
5 Lviv
6 Lviv Budapest non stop on Ryanair for about $50
7 Budapest
8 Budapest
9 Budapest requires at least 3 full days.
10 Budapest to Vienna on the morning train
11 Vienna
12 Vienna to Prague on a late day train
13 Prague
14 Prague
15 Prague to NYC
Now choose day 16 in either Prague or Vienna or Kyiv.
The old standby tour:
1. NYC to Prauge
2. Arrive Prague
3. Prague
4. Prague
5. Morning Prague to Cesky Krumlov by Bean or CK Shuttle
6. Afternoon Cesky Krumlov to Vienna by Bean or Ck Shuttle
7. Vienna
8. Vienna / Melk
9. Vienna
10. Morning Vienna to Gyor by train – Taxi to Archabbey / winery at Pannonahlma
11. Gyor to Budapest by afternoon train
12. Budapest
13. Budapest
14. Budapest
15. Budapest to NYC
Now choose day 16 in either Prague or Vienna or Budapest
