It's best to do it at the college that you plan to attend if that's possible and reasonable. Many future cadets interview at a nearby college when their college of choice is too far for travel to it.
DS also did his at a local college. Didn’t hurt him. He is now a sophomore in his 2nd year of his 4 year ROTC scholarship. He did, however, visit and meet with the Cadre at the schools he was most interested in.
For NROTC, my DS did his interview at a nearby office for Navy Officer Programs. He was fortunate to connect with an enlisted recruiter who made the effort to help him navigate the NROTC application process.
I think most applicants dont realize that the PMS assignment to the respective university is a maximum of 2 to 3 years. They all want their programs to do well but their first loyalty is the Army. So if you are a great candidate who would serve the Army well then the PMS will be willing to endorse you regardless of your preferred institution.
I wish what emwvmi01 says above could be true in every case, but that was not our experience . . . my advice is to go interview with the PMS at the school you want to attend if you can.