You would not be allowed into the prison. Prisons are controlled-access areas; no one goes in or out without an official purpose, for reasons that should be fairly obvious. Journalists who want to enter the prison have to ask for permission from prison authorities, and the authorities are well within their rights to deny access entirely or impose any restrictions they think are justified. Normally, access to cell blocks is going to be denied entirely. Not even defense attorneys have a right to visit their client's cell; they have a right to visit the client, but the prison staff can (and typically does) set aside rooms for visits.
Would I file something similar to a freedom of information request?
No. FOIA requests are authorized by law and the agency must respond, while a visit to a cell block is entirely up to the discretion of authorities. Your best bet would be to contact the relevant public affairs office, but be prepared to hear "no." You could try to contact your members of Congress and see if they could put some pressure on, but it's unlikely that'll help. FOIA itself allows you to request records that already exist, but not to request the creation of new records. You could ask for photos that have been taken of the cell using a normal FOIA request, but you could not ask the BOP to take photos.