Most of metropolitan Nablus is small enough to be navigated on foot, and it's not recommend that you wander too much as there is a number of neighborhoods in Nablus that may have troubles with IDF raids. It's best to simply stay in commercial districts, don't wander into any residential areas that you don't have any business being in unless you are proficient in Arabic or English.
The public transportation in Nablus is informal, and normally is done by sharing servees taxis. The black-and-white taxis sometimes with a Hebrew "Monit" sign on top will take you anywhere in Nablus, and it's easy to find people to share the taxi with for many locations.
