Within means not outside a place.

Pattern: be + within + noun
Those schools are within the county jurisdiction.
There is too much commotion within the building.

Typical nouns used after within:
area, building, city, country, county, jurisdiction, state, territory, wall

Within means less than a period of time.
I will return within the hour.
He will finish within five minutes.

Within means less than a distance.
There is a hospital within five miles of the school.
The storm was within ten miles of our town.

Within means possible; not exceeding the limits of something.

Pattern: be + within + (one's) noun
At last, the beach is within sight!
A fortune is within our reach if we are lucky.

Typical nouns after within:
bounds, hearing, range, sight, reach, the law, the limit, the rules

Expression

to keep within the family—to not reveal something to anyone who is not a family member
That man has a strange history, but they keep it within the family.