Seems as if you can make good train connections from all directions thru Rzeszow. The train stations seemed confusing to me because I don't speak the language and I found the schedules on the wall pretty useless for this reason. I would suggest that you know which train you want and be ready to ask for the right ticket. We were lucky to have people helping us to get on the right trains each time.
No mishaps, tho. Once on the train, we found them comfortable and the food was surprisingly good. We enjoyed the trip back to Warsaw...seeing wonderful farmland and forests along the way. My husband stood at the window looking for deer almost the entire time we were on the train.
The train and bus stations are together on ul. Grottgera -- it's about 500m to the Rynek.
There are many daily trains to Przemysl to the east and to Tarnow, Krakow etc to the west. There are 2 or 3 trains a day to Warsaw.
If you want to go to Kosice (as I did), then you have to take a train back to Tarnow to pick up the Krakow-Kosice train there.
Next to the train station on ul. Grottgera about 500m from the Rynek.
Services to Przemysl, Sanok, Krosno, Zamosc, Lancut, etc. -- and one a day to Warsaw.
The are no buses to Slovakia -- the service to Kosice stopped a couple of years ago.
The best way to get to Rzeszow is by train. Whereever you are in Poland you can take direct train to Rzeszow via Krakow or indirect one with change in Krakow. There are also some direct trains from Lublin and Lvov (Ukraine). Prices vary depending on type of class and type of train - all between 5 - 8 USD. Alternatively there are direct road connections with Poznan via Wroclaw, Katowice and Krakow; with Warsaw via Lublin. If you are still outside Poland and plan to take flight it is worth to consider LOT polish airlines since you can have a free flight from Warsaw to Rzeszow.
Travelling by coaches takes takes most of time and is generally inconvinient.
Moving within and around Rzeszow is not as challangeable as getting there. Some foreign tourists may be nicely suprised by the taxi charges. Since Rzeszow itself is not a big city it is convinient to use bicycle or local buses (MPK - usually red ones) to moving from one location to another. Each bus stop is equipped with route timetable and full info about bus route. To avoid any misunderstandings with bus service is advisable to buy full price ticket. It is better, however to take taxi during evening or night trips. A taxi driver can pick you up from any location within the area of city as well as from reasonable distance around the city. Call taxi (RadioTaxi) companies often have operators that can speak in foreign languages. They are generally perceived to provide better service than private taxis. Useful websites and numbers:www.mpk.rzeszow.pl - local tarnsportation company, site icludes map of Rzeszow ('Mapa' button), tel number 919 or 9622 - taxi companies, numbers can be dialed in any city nationwide.
Moving around Rzeszow could be more complex as there is more choice of means of transportation. It is reasonable to use train service (PKP) to get to such destinations as Krakow, Przemysl, Lvov (Ukraine) or Przeworsk. Ticket's price varies between 1,5 and 4 USD one way. When going to Lancut, to Solina lake, or to Bieszczady mountains is better to use local coach service (PKS).Their coaches stop in the centres of town and cities throughout coach route and they cover wider range of destinations in the area. Renting a car gives you mobility and it is definietely the fastest way to moving around. It is not however reasonable to use car if you plan to have combined travelling-walking trip in Bieszczady mountains.
Useful websites and telephone numbers: www.pks.rzeszow.pl - local coach service (PKS) website, includes timetable ('Kraj'/'Dworzec Glowny' buttons); www.polrail.com (PKP) (national train service, eng.)
You can take a plane to Rzeszow city LOT polish airlines and take a public bus to Ustrzyki Gorne or Solina city.
Also You can take a train from Warsaw to Zagorz city and take a bus to Ustrzyki Gorne or Wolosate village.
public buses, on foot :-)