I grew up in NY and I never had a need to take the subway into the Bronx. I don't see any reason he would need to- even to buy drugs. You can do that in Manhattan. I'm thinking he could have gotten lost or been meeting someone there, but if he went to NY with these 2 girls and didn't know anyone else in NY, who else would he be meeting? The fact that he told his roommate he was "stepping out for the night," but didn't take his cell, sounds like he had a plan and wasn't coming back until the next day and didn't want to be disturbed. Those female roommates might also know something more than they have said, even if they think it's trivial.
I agree they need to check with Burger King to see the cam and find out if that's actually him using the card and if it is, who else is with him. As for LE not thinking it's foul play - they always say that. It's the easy out for them as they feel so overworked and it's the way they can say they did the best they could without doing the best they can.
Also, idk if he ever mentioned anyone in NY or a girl from NY to his family or friends, but it's possible he could have made contact with a person and arranged to meet up when he got to NY and not mentioned it to anyone not knowing how it would turn out. Maybe check his laptop and his pc and phone to see if he has anyone in it who is from NY (e-mails, im's anything). I'm guessing LE or his family might have done that already but jic no one has, do check.
I hope you find him soon and he's ok^^