passer par -- to go/pass through/by. It is used to specify a location that your path touches or passes by. Like, e.g., a stop on a route.

Sur mon chemin du retour je passe par la boulangerie. -- On my way back I pass by the bakery.
Le train passe par Paris. -- The train passes through Paris. It means that Paris is a point along the route of the train, not necessarily that the train cuts right through the city.

passer à travers -- to cross. This means that you emphasize going through a town or a place.

Je dois passer à travers Paris pendant l'heure de pointe. -- I have to cross Paris during the rush hour.