Getting to the Carpathians
Ivano-Frankivsk is a good starting point for destinations into the Carpathian mountains. The Kyiv-IvanoFrankivsk train (#204) arrives at 8:40 AM. A convenient connection is the IvanoFrankivsk-Rakhiv train which leaves at 9:15 AM and goes through Yaremche, Tatariv, and Vorokhta. Other train connections throughout the day are: Vorokhta (3 hour ride, 3 per day), Kolomiya (2 hour ride, 11 per day). If you would like to visit the Kosiv or Verkhovyna regions then you need to take a bus from the station immediately to the left of the train station. Bus connections are: Yaremche (2 hour ride, 12 per day), Vorokhta (3 hour ride, 6 per day), Kosiv (3.5 hour ride, 11 per day), Verkhovyna (4.5 hour ride, 6 per day). Of course, taxis are more convenient and will be happy to be of service. Approximate rates are: Yaremche $20 (1 hour ride), Kosiv $30 (1.5 hour ride), Verkhovyna $40 (2 hour ride).TO GET TO THE CARPATHIANS FROM LVIV
The Lviv-Rakhiv train is convenient because you can get to Ivano-Frankivsk, Yaremche, Tatariv, Vorokhta, and Rakhiv without changing trains. Unfortunately this train is one of the worst in the system. It travels quite slowly because the track is also not in very good condition.
Other trains departing from Lviv that go through Ivano-Frankivsk and Kolomiya are:
Lviv-Chernivtsi
Uzhgorod-Chernivsti
St Petersburg-Sophia
Peremyshl-Chernivtsi
These trains leave Lviv early in the morning:
Kyiv-IvanoFrankivsk
Brest-IvanoFrankivsk
Minsk-IvanoFrankivsk
Busses are also a possibility, although they require more familiarity with the complications of traveling in Ukraine. There are approximately ten busses per day that go from Lviv to Ivano-Frankivsk. There is more than one bus station in Lviv and the main bus station is located quite far from the train station.
From Poland there are several convenient overnight bus routes that arrive in Ivano-Frankivsk. In Poland, the city of Ivano-Frankivsk is often referred to as Stanislaviv, the original Polish name of the city.
Peremysh-Kalush
Warsaw-Kalush
Warsaw-Dolyna
Warsaw-Kolomiya
Tomashiv-Kolomiya
Lublin-Kolomiya
Peremysh-IvanoFrankivsk
Avoiding the Ukrainian transportation system can be avoided by hiring a taxi driver to take you from Lviv to Ivano-Frankivsk. The cost should not exceed $30 for the ride, although drivers will, of course, be happy to take more. Their insistence on taking more is probably related to the degree that you advertise yourself as a "wealthy foreigner".