Have Been Around Meaning
(idiomatic) To be experienced in worldly matters; to be seasoned, not naive.
Example: 1900, Edward Stratemeyer, The Rover Boys Out West, ch. 17:
"Oh, I've been around a little before," said Tom coolly.
"Yes, you look like a lad who has seen something of the world."
2008, "'Special Report' Panel on Hillary Clinton's New Campaign Advertisement," foxnews.com (US), 3 Mar. (retrieved 1 Jan. 2009):
Barnes: John McCain has been tested. He has been tested in war, and he passed that test. When has Hillary been tested? She has been tested in her marriage. That's about it.
Williams: You're being very mean.
Barnes: No I'm not. I'm being honest.
Williams: She has been around. She has met world leaders.