Nablus is a Palestinian city in West Bank.
Hitchiking out anywhere
All the local or regional traffic consists of shared taxis. First take a shared taxi to cross the checkpoint. After the checkpoint you can hitch anywhere. You might be picked up by Jewish settlers or Israeli Arabs.
Yo can go almost everywhere from Tapuach junction, which is very close to Nablus. You can try to stop any car in Nablus, even inside the city, or just pay a taxi there. It would be between 10-20 shekels. If you hitchhike an arab car, maybe he won't understand English and neither hitchhiking, so probably he will call a friend or he will stop someone on the street to talk with you.
From Tel Aviv take bus 127 which comes from central bus station ,get down at second but last stop .walk on to the No5 highway and hitch in on-ramp.