Following this Question, where Nij answered about the medals, that they can be placed where the club wants them, not like the replica trophies, I would like to know, where can the clubs place those trophies?
This is answered by the same section of regulations as that question, where article 11, section 11.02 states that
[r]eplica trophies awarded to winners of the competition (past and current) must remain within the relevant club’s control at all times and may not leave the club’s country without UEFA’s prior written consent. Clubs must not permit a replica trophy to be used in any context where a third party (including, without limitation, their sponsors and other commercial partners) is granted visibility or in any other way which could lead to an association between any third party and the trophy and/or the competition. Clubs must comply with any trophy use guidelines that the UEFA administration may issue from time to time.
the real trophy will go where UEFA the organisation puts it
the replica trophy must stay in the club's home country, unless they get permission to move it
the replica trophy must not go anywhere that makes it appear some third party, such as a business, has a relationship with the trophy or with the the championship
UEFA will make further detailed rules for where and how to keep the trophy, but these are not apparently widely available