Radom is a city in Poland.
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North towards Warsaw (S7)
The best way to get out of Radom is to take bus 15 or 25 until the stop just after the big roundabout on the road Warszawa-Kraków road. You won't miss it, you will see a sign "Kraków" or "Warszawa" before the roundabout. There is a petrol station and 2 bus stops where cars and trucks can stop, one on the way to south, one on the way to north.
Note: the road through the city is unsuitable for hitchhiking (little bus stops, no shoulder). If you're only travelling through Radom rather than to the city itself, ask the driver to drop you at the city limits rather than inside the town. Otherwise you'd have to walk some 40 minutes to either limit of the town.
South towards Krakow (N7)
Take a bus number 5 (direction Pruszaków) and get out at the stop Kielecka/Halinowska just after a roundabout. Here is great place for hitchhiking, a sign "Kraków" or "Kielce" will be helpful.
Take a bus number 8 in the direction Kierzków and get out at the stop Wolanowska/Areszt (you have to press a button to ask the driver to stop). Here is great spot to hitchike to Wroclaw, Lodz or even Poznan. The best way to start is write a sign "Piotrków" to get to the town of Piotrków Trybunalski, where you can interchange in any direction written above.
East towards Lublin (N12)
Take a bus number 9/10/17/21/26 and get out on Kozieniecka/Żółkiewskiego bus stop. You will see big roundabout with bus stop on direction to Lublin. Writing "Lublin" is good idea.