Usage of "take somebody to somewhere"

Take, in the sense you are describing, means to accompany someone to a certain location. That's about as far as it goes. When you "take" someone somewhere, you don't necessarily need to invite them.

"Take" is a fairly common verb in the English language. It's used very often in informal speech. Examples:

"I will take you to your room now."

He looked around and realized Joel had taken all of his friends to the fair.