If you just want a short, day of fun, then the left-right game is good for this. At each junction you get to, just alternate taking the left turn/right turn, and see where you end up.
Otherwise, we had fun where a few of us were on Easter holiday from University in our first year, so we thought we’d have a roadtrip. I drove down to pick people up, all from around different areas of the UK, so as the trip went on we gathered more people. We had vague ideas of where we wanted to go (i.e. to pick people up) but other than that, didn’t make any decisions on where to spend our days/nights until everyone was in the car.
After driving from the Midlands, down through Oxford to Southampton (me + 2 others at this point), we headed west across to Dorset to pick up person number four. Some nights we camped by the beach, others at peoples’ houses.
I think by the end of the trip, which only last three days (the UK’s not that big) we’d totalled up around 900 miles, all of which were fun-filled _
In a couple of months I should be doing pretty much the opposite: there’s a charity event called “Bum it to…”, this year it’s Bucharest. So in March I should be attempting to hitch-hike from Sheffield, UK to Bucharest, Hungary. All we have is the destination, with no means of getting there!