If you all meet up at the house before or after and its in your budget, pay to have a stripper (or 2) come crash the chips and dip fest. Yeah thats generally reserved for "bachelor party" but screw it rub it in. Its been the same experience with my friends actually. (Yes people do wear on each other after a while). My advise is celebrate YOURSELF LEAVING that. AFTER moving on, just DO ANYTHING, solo and whatever. The best decision is the one already happening - getting outta there with brighter things ahead.
If it has to be a day trip then I guess camping is out. Primitive camping is a blast. My buddies and I have done it semi-regularly for years. You could do a hike, which might be fun. Paintball could be good. If you were on the west coast, I would suggest wine tasting. Too bad you can't rent a beach house. We've done that several times as well. It isn't even about the beach as much as it is about playing cards, dominoes, drinking, making good sea food, grilling out and that type of stuff. If you do that, then some people can go to the beach during the day, and other can lounge around and play horse shoes or whatever. Once we chartered a fishing boat and went fishing. That was fun. You could do that. With six guys it might not be too much, especially if you don't charter a private boat but reserve six spots on a public charter. Go see a professional baseball game. Sometimes a really nice restaurant is a great experience in itself. That might not be cheap though. A Karaoke night can be fun, if everyone has the proper "don't give a f***" attitude about it. Pick out a couple of songs that all the guys can do together, and just laugh and appreciate the other people participating at the place you go. Find a place to go go-cart racing. Go nerdy and plan a D&D night and order pizza and have beer and cocktails while your playing. I don't know. I wish you luck.
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I think they're looking for something different to do other than what would otherwise be known as "Tuesday".