I’m a current day student at Lawrenceville, which has a 70/30 boarding-day ratio.
Due to the house system, day students are pretty well integrated into campus life; just like the boarders, we hang out in the common rooms, go to feeds, participate in Olympics, etc. I personally am actually friends with mainly boarders, and I remember struggling to come up with the names of four day students when doing my housing card at the end of last year. While you’ll get some small fraction of boarders saying “lol imagine being a day student,” that’s pretty much the full extent of what’ll happen to you. Other than that, we’re basically identical to the boarders—pre COVID, I would spend 12+ hours on campus on weekdays, and stay until 11 PM each Saturday (you can even sleep over if you’d like). Some day students even stay through study hall on weekdays (ending at 10pm), because it helps them work, so there’s no real limit to what you can or can’t do.