How to have a fulfilling social life as an academic
The special thing for you coming out of (what seems) a pretty demanding grad school time is that being a postdoc is not so special at all. In most ways, being a postdoc is not unlike any other time-demanding job. You come to work in the morning, spend most of your day there, and, in the evening (whenever that is, time-wise), you will more often than not go back to your home and stay there to relax a bit. You bond with your co-workers, but usually more in an "acquaintance" than in a "friends-for-life" way.

Anyway, it seems to me that you are thinking that you can only hang out with people on your academic "level". This has never been my personal experience at all. In all my work places, grad students often hang out privately with the postdocs that they work with, and many of the younger faculty staff often join in for ad-hoc parties as well. I guess it is all a question of how you want to appear towards your junior work mates. There are people that see fit to construct an image of aloofness towards their students, and others like to mingle. Nothing wrong with either, of course, as long as your work relationship stays reasonably professional.