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.