Americans and most Europeans do not need a visa to travel to Ukraine for up to 90 days.   All you need is your passport and an airline ticket.  We recommend that you fly to Kyiv even if you are more interested in living in a different city.  Stay in a hotel for 1 or 2 nights and then make your plans for the rest of your trip.

Most US airlines fly to Ukraine through one of their European partners.  This of course results in frequent flier miles.  The only nonstop flights are on Ukrainian Airlines from New York.  In spite of much better service and passable food, it is still a long and difficult flight, even nonstop on UAL.  Do not take a flight with 2 stops, you will be sorry.  Turkish Airlines is a reasonable alternative especially if they still allow you to take 2 big suitcases.  You should expect every seat to be full on the airplane and you should expect the lavatories to be filthy by the time you arrive, so take it easy on what you eat and drink before and during the flight.

If you are bringing more than $10,000 dollars into Ukraine then you need to fill out a special form and say why you are carnying so much money.  For example, if you are planning on buying an apartment or house.  It is not a problem but you will need to go though a special line in Customs.  Visa and MasterCharge and smart phones tied to a credit or debit card are widely accepted but paper cash is still popular.  You can open a bank account here and have a debit card in either UAH or Dollars.  American Express and other credit cards are rarely accepted although there are ATM's that will give you cash on your American Express card.

Within Ukraine there are local flights between Kyiv and most of the major cities.   Most Americans will be happiest in Odessa and the beaches south of the city, Lviv and Ivano-Frankivsk.  Lviv was a Polish city before the borders were moved and is considered to be Little Prague.  A little closer to the mountains is Ivano-Frankivsk and of course you might consider one of the small cities in the mountains.

Most Ukrainians take the train rather than drive or fly.  It is less expensive than driving and Ukraine is surprisingly large.  You definitely want to go first class though.  Roads are not crowded but are not up to US standards.  It will take longer to drive than you expect.

Within cities, taxi's and Uber and Uklon and Bolt are everywhere.  They cost less than in the USA too.  There are buses and trolleys and the Metro (subway) in all cities and also inter-city buses.  Public transportation is cheap.  Avoid the mini-bused (Marshrutka's).  Uber also has shuttles.