If you're in town during football season, try to go to a game. I have been to the stadium in many capacities-as a HS student selling concessions for my marching band, as a member of the Blue-Gold All-Star Band (this is a summer charity event), and as a "fan". It is a small university, but they enjoy their football games. And, if for no other reason, than to see the "ass-kickin chicken" (as UD students like to call their mascot, the Fightin' Blue Hen)!
UD is home to some of the top notch world ice skating athletes, and has a wonderful public ice rink right next to the football stadium. For a couple of bucks, you can go and skate on the same ice that many of these people train on. I believe there are also times when the public can go watch the sessions, but I don't know all the details of this. A totally fun family and friends activity!
The local McDonald's is known as the local attraction for university students. The story is that Kurt Cobain (of rock band Nirvana) once stopped here for lunch. He cut through the line with the typical 'I don't have to stand in line, I'm a famous rock star,' attitude, so the students beat him up. Thus, this will soon go into the atlas of History of the New America as 'the place Kurt Cobain got beaten up by local students.'