To go out and do things you consider fun with people you know.
La'Kisha: Hey Danny, what you doin tonight?
Danny: I think Hunter and I are going to pal around in Benton County.
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To ignore work responsibilities and instead just hang out with people and find other obligations that you can call "work".
Billy likes to Pal around every week. Billy was supposed to take care of setting up for the work picnic on the weekend, but instead he was palling around getting breakfast and lunch on work's dime with many people and ignoring actual responsibilities.