Flying can be a very social avocation. You could fly just yourself and a passenger, but you're joining a fraternity of many thousands who enjoy not only flying but talking about it. If you get heavily into aviation you'll soon find that many of your closest friends are pilots.
Fly-ins are the most popular social events for pilots. Fly-ins can involve a few friends meeting for breakfast or a picnic together at a small airport, or can turn into big get-togethers with thousands of participants coming in from neighboring states or even across the country. Fly-ins are simply excuses to go flying and meet other like-minded people. You can find out more about fly-ins through clubs and national and regional aviation magazines. On any given weekend there's probably a fly-in within a couple hundred miles of where you live. If not, call your flying friends and get one started.
Pilots enjoy flying off to other airports and finding a nearby restaurant for a meal. They call these trips "hundred-dollar hamburgers". Thanks to smaller, simple aircraft, they may be referred to as "fifty-dollar hamburgers".
Joining the EAA, AOPA, and other groups will motivate you to find local chapters and participate in various charity events. Private pilots can take people up for charity flights (donations going to a charity). Ask the FAA or your flight instructor for specifics.
Of course, there are national and regional conventions that you must attend. Planning for such events can be fun and instructional as you apply what you've learned about cross-country flying toward a specific goal.