@paok1970,
To run through a place means either
A. Actually transport yourself from end of the place to the other.
B. To get exhaust all that the place has to offer you, such as, "I went through every store in town but still couldn't locate a magnifying glass stronger than 2X magnificiation."
To run across a place means to find it by accident. Such as: "My job sent me to Brooklyn for a day, and while there I ran across this bakery with the most delicious torte cake."