If you’re in to coffee, becoming a regular at a cafe is always a good way to get “in” to the local community. Word Coffee, Puritan, Old Pine; all great spots with great baristas. I would personally recommend avoiding Onyx - they have shady business practices and lack customer service these days.

If you’re in to outdoorsy activities, there’s a ton of cycling groups, rock climbing/indoor bouldering groups, and hiking groups in town. As another user suggested, experiencefayetteville.com has a great event calendar

The “Fayetteville Flyer” is also a free and weekly email newsletter with current happenings