Desiring God posted this article from 1983 by John Piper. It's called "Toward a Theology of Church Picnics." In the article, Piper explains some of the theological reasons for getting together as a church outside of regular church hours just for hanging out.
While I didn't articulate them to the church as well as Piper does in this short article, these are the exact reasons why we hold a Family Night ministry at Riverview.
The theme verse for our Family Nights (at least this summer, and perhaps on into the future) is 1 Thessalonians 3.12 - "...and may the Lord make you increase and abound in love for one another and for all..." In my opinion, the only way you can really "increase and abound in love for one another" is if you spend time with people and get to know them. Yes, Sunday mornings offer a bit of this kind of interaction, but not really enough. A lot of the interaction that takes place between people between Sunday School and the service pretty much takes place on the surface.
I think just getting to know each other is a huge part of our ministry at Riverview. The more we know each other, the more we love each other, the more united we become in Christ. So yes, there are some pretty deep theological reasons for having a church picnic.