Our typical layover, Longhaul, would be mostly just under 24 hours ( basically a night stop), with a few of 48 hours ish slips where you get a clear day. As far as social contacts go it's pretty much what bafanguy said.
Even when you factor in the fact that unlike his outfit we "only" have 4000 plus pilots, total, with maybe 1000-15000 ish on the type I'm on, the following is still true for us:
When you factor in people going on vacation, training, sick out, contractual provisions to drop/swap trips it's possible to fly a trip with someone and, with no exaggeration, never even see that person so much as walk through your field of vision...ever again in your life.
Similar deal for the cabin crew we work with (>10,000), there's a handful of the seniors you might see once a year but other than that it's possible to go 15-20 years before meeting up with a cabin crew member who you shared a beer/glass of wine with.
In short at a large airline don't expect a forces style crewroom familarity and seeing the same buddies everyday culture...it can be very different.
As for activities - TBH once you've been somewhere a few times and seen the elephant/done the tour then it's each to their own, some use time off down route to get over fatigue and probably won't rush out with their new best mates every on every night stop, I think as PM has said it's a combination / mix of " walks, hire bicycles, watch a flim, go to the pub or simply do nothing. There's no rank, just a group colleagues who will try and make the best use of the time we have down route."