Next week, Burkett, a 6-foot-4, 271-pound offensive lineman from Jacksonville (Fla.) Bartram Trail, is scheduled to visit Stanford. He'll travel to Georgia Tech a couple weeks after that.
In addition to the three aforementioned schools, Burkett is considering Purdue, Vanderbilt, and a couple of schools in the Ivy League. He attended a game at Vanderbilt last football season and visited Princeton during the spring.
With the exception of Stanford, Burkett says he's been offered by every school he's considering.
In the midst of taking his summer visits, Burkett doesn't have a leader.
"Hopefully before school starts I'll be able to make a decision," Burkett said. "That's what I'm planning on."
Having had wrist surgery a few days prior, Burkett never planned to participate in Fedora's Freak Show. And then his travel plans forced him to miss the elite camp entirely.
"We were there for about three or four hours before [Fedora's Freak Show]," Burkett said. "We got to meet everybody and looked around campus a little."
Dan Disch, who recruits the Jacksonville area for UNC, gave Burkett and his family a full campus tour.
"We went through all the historic places – like the Old Well," Burkett said. "And of course we saw the facilities.
"As a whole I really liked it."
Following the tour, Burkett separated from his family to have a one-on-one meeting with Chris Kapilovic, UNC's offensive line coach.
"He let me know that they didn't have a whole lot of spots left, because they only get 20 scholarships this year" Burkett said. "Other than that, he talked to me about how he does things with his O-line and what my role would be."
Burkett said Kapilovic's comments about UNC's class made him feel he needed to approach his recruitment with more urgency.
"It does make me kind of want to hurry things up, because I realize a lot of schools are going through the same things right now," Burkett said. "But I still have a lot of thinking to do. I just hope I have enough time."
For Bartram Trail, Burkett earned a starting spot at left guard as a sophomore. He moved to left tackle for his junior season.
"Most [colleges] say they want me at tackle because of my footwork," Burkett said. "A couple of schools have asked me if I can play center, so that might a possibility as well."
Kapilovic told Burkett that he likes his versatility and the depth chart will determine his role at UNC, but that he'd start off at offensive tackle.
Burkett and his family concluded their stay in Larry Fedora's office for a meeting with UNC's head coach.
"He was just kind of explaining his head coaching philosophy," Burkett said. "They're really focused on building up their players into men. Of course football is important, but for him, he said, is making a man out of his players is most important."