I think familiarity breeds contempt most times. I'd like to show up with a reasonable amount of time in advance for a setup and soundcheck. Once that's done I prefer to vacate the place if it's more than a half hour before you go on. Ask how early before the show they want you back, and then scoot. Take a walk, grab a burger or smoke, scope out the block, hit a bookstore if you're lucky enough to see one close by, or whatever. Then return 15-20 mins before showtime. When done I think it's essential to pack up and load out as quickly as possible.
Most places I've played seem to prefer you get in and out fairly quickly. End of shift, most employees just want to go home. And the club owners want the staff off the clock earlier rather than later since time is money. (Minor point: the female staff have been hit on so many times by the patrons and band members most nights that they usually don't want to get to know anybody by the end of the evening. So spare them all your best opening lines. They've heard them all at least a hundred times before.
All of them. So if you really want to impress that exceptionally cute bartender, the best way to do it is: Don't even try.

)
Post show, my rule of thumb is unless somebody with influence - like the manager or the owner -
specifically asks us to hang, we don't presume on the hospitality of the house. We pack out, collect our money, skip the drink, say our thanks you, leave our business card and current open dates, and get the heck out.
I've found the less you try to act like buddies, and more you come across as competent and trustworthy employees, the more the places tend to ask you back.
Other's experiences may be different than mine. But this is what I've seem most times. There are exceptions to the above. But the number of times I've seen bands turn management off by acting overly familiar with the boss and staff, or hanging out too long afterwards, are too many to for me to count. The number of bands I've seen hurt themselves by acting totally pro, getting in and out fast, and keeping the chit-chat and schmoozing to a minimum after a show is: zero times.
YMMV.