I'm not sure there are specific restaurants geared for young adults of that age. I am 22 and enjoy the same places the average adult likes, including signature establishments. My girlfriend and I celebrated our college graduation last month with a quick trip to Disney, and we had dinner at Jiko and 50's Prime Time Cafe.
I suppose with young adults, particularly men, I would avoid the character meals. Otherwise, it depends on your group's preferences and palates.
If it helps, my favorite restaurants on property include Boma, Kona Cafe, Jiko, 'Ohana, Kouzzina and Coral Reef.