Nădlac-Nagylak border crossing
<map lat='46.167367' lng='20.721402' zoom='11' view='0' float='right' height='270' width='350' />
The Nădlac-Nagylak border crossing connects Hungary (near Szeged) with Romania (near Arad). On the Hungarian side is the village of Nagylak, while on the Romanian side is a town called Nădlac.
East into Romania
The border is about 50 km from Arad, and the majority of cars are going there. There is also heavy truck traffic. For hitchhiking there is a parking lot for trucks just after the border. 400 m further on there is a gas station.
If your driver does not go as far as you need to go, do your best to get dropped off at the border crossing itself and not at a gas station or rest stop after it. There are usually beggars (or robbers) there and they will give you a hard time. You'll get offered more money than rides by the tourists going through with full cars, but at the end of the day you'll still be stuck. Many languages are useful here, like French, Spanish and definitely German.
West into Hungary
Szeged is about 50 km away on national road 43. There is a new bypass highway around Szeged so it is not recommended to stop there.
There are decent hitch hiking spots within 1km of either side of the border so cross on foot and continue looking for a ride from the other side.