West in direction of Lausanne
In the west of the city there is a roundabout with an on ramp to the highway (which goes only a few kilometer though). It is about 2km from the city center along the main street Gliserallee. Cars go quite fast, but in direction of Lausanne there is plenty of space to stop. There is also a gas station at the round about.
South-East in direction of Domodossola, Italy
The bus stop Brig, Geschina in front of the municipal open air bath is a good place to hitch from. It's just a few hundred meters from the center along the Neue Simplonstrasse. The bath is very refreshing as well, if it should take longer. Don't hitchhike onto the highway from the round about mentioned above, there it is hardly possible to stop.